Please help in finding the radians in degrees!

Ok, what's the full question here

Answer:

  f)  a[n] = -(-2)^n +2^n

  g)  a[n] = (1/2)((-2)^-n +2^-n)

Step-by-step explanation:

Both of these problems are solved in the same way. The characteristic equation comes from ...

  a[n] -k²·a[n-2] = 0

Using a[n] = r^n, we have ...

  r^n -k²r^(n-2) = 0

  r^(n-2)(r² -k²) = 0

  r² -k² = 0

  r = ±k

  a[n] = p·(-k)^n +q·k^n . . . . . . for some constants p and q

We find p and q from the initial conditions.

__

f) k² = 4, so k = 2.

  a[0] = 0 = p + q

  a[1] = 4 = -2p +2q

Dividing the second equation by 2 and adding the first, we have ...

  2 = 2q

  q = 1

  p = -1

The solution is a[n] = -(-2)^n +2^n.

__

g) k² = 1/4, so k = 1/2.

  a[0] = 1 = p + q

  a[1] = 0 = -p/2 +q/2

Multiplying the first equation by 1/2 and adding the second, we get ...

  1/2 = q

  p = 1 -q = 1/2

Using k = 2^-1, we can write the solution as follows.

The solution is a[n] = (1/2)((-2)^-n +2^-n).

Answer:

x = -2

Step-by-step explanation:

subtract the 6 from 22

then divide -8x and 16 by -8

then you get your anser

The solution to the equation 6 - 8x = 22 is x = -2. The equation was solved by rearranging and isolating 'x', and then dividing by the coefficient -8.

The question is a simple linear equation. Let's solve it step by step:

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Answer:

  (-5, 0) ∪ (5, ∞)

Step-by-step explanation:

I find a graph convenient for this purpose. (See below)

__

When you want to find where a function is increasing or decreasing, you want to look at the sign of the derivative. Here, the derivative is ...

  f'(x) = 4x^3 -100x = 4x(x^2 -25) = 4x(x +5)(x -5)

This has zeros at x=-5, x=0, and x=5. The sign of the derivative will be positive when 0 or 2 factors have negative signs. The signs change at the zeros. So, the intervals of f' having a positive sign are (-5, 0) and (5, ∞).

The details provided do not correspond to a coherent mathematics problem regarding the function [tex]f(x) = x^4 - 50x^2 + 3[/tex]. Therefore, an accurate response cannot be provided without further information or correct context.

To address the question about the function [tex]f(x) = x^4 - 50x^2 + 3[/tex], we need to analyze its intervals of increase and decrease, as well as find any local extrema and points of concavity. However, the question as posed does not provide enough context or coherent detail for the actions requested, such as finding the inflection points or intervals of concavity, since no specific function was clearly defined. Instead, various unrelated Mathematics problems are listed, each of which is missing comprehensive details needed to provide an accurate answer.

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Answer: yes, GM is expected to provide performance greater than 123

Step-by-step explanation:

b) It is expected that the GM achieves a performance greater than 123. This situation occurs because 123 is less than the average for GM but is greater than the average for Regular. Thus we observe that P (performance> 123 | GM)> 0.5 and P (performance> 123 | Regular) <0.5

Answer:

99

Step-by-step explanation:

11 crows : 3 hawks

363 crows: X hawks

X/363 = 3/11

X = 363 × 3/11

X = 99

Answer:

Step-by-step explanation:

Given data

Average sales = 8000

n = 64

standard deviation = 1200

      8300

The solution is attached in the picture below

Answer:

The attendance on tuesday, october 4, is of 144 people.

Step-by-step explanation:

The attendance after t days is given by the following equation:

[tex]A(t) = A(0)(1-r)^{t}[/tex]

In which A(0) is the attendance on the first day and r is the daily decrease rate.

Premieres on saturday, october 1, and 420 people attend.

This means that [tex]A(0) = 420[/tex]

Attendance then decreases by 30% each day.

This means that [tex]r = 0.3[/tex]

So

[tex]A(t) = A(0)(1-r)^{t}[/tex]

[tex]A(t) = 420(1-0.3)^{t}[/tex]

[tex]A(t) = 420(0.7)^{t}[/tex]

Find the attendance on tuesday , october 4

This is 4-1 = 3 days after saturday. So this is A(3).

[tex]A(3) = 420(0.7)^{3} = 144[/tex]

The attendance on tuesday, october 4, is of 144 people.

To find the attendance on Tuesday, October 4, after a 30% daily decrease from an initial attendance of 420 people on Saturday, October 1, we calculate the exponential decay for three days to get approximately 144 attendees.

The student's question involves an exponential decay math problem where the attendance of a play decreases by a percentage each day. To calculate the attendance on Tuesday, October 4, we begin with the initial attendance of 420 people on Saturday, October 1. We then apply a 30% decrease for each subsequent day:

Since we cannot have a fraction of a person attending, we would generally round to the nearest whole number, which means about 144 people attended the play on Tuesday, October 4.

Rejection region(s)

t > 2.998

Test statistic value

t = 2.89

Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Option B is the right choice.

State the hypotheses

H0: μD = 0

Ha: μD > 0

State the rejection region

Since the alternative hypothesis is one-sided, we use a one-tailed test. The rejection region for a one-tailed t-test with significance level 0.01 and 7 degrees of freedom is:

t > 2.998

Compute the test statistic

The test statistic for a paired t-test is calculated as follows:

t = ([tex]\bar x[/tex]D - μD) / (sdD / √n)

where:

[tex]\bar x[/tex]Dis the mean difference between the unabraded and abraded breaking loads

sdD is the standard deviation of the difference between the unabraded and abraded breaking loads

n is the sample size

Calculating the mean difference:

[tex]\bar x[/tex]D = (36.3 - 28.5) + (55.0 - 20.0) + (51.2 - 46.0) + (38.6 - 34.0) + (43.2 - 36.5) + (48.8 - 52.5) + (25.6 - 26.5) + (49.6 - 46.5) = 6.85

Calculating the standard deviation of the difference:

sdD = √[((36.3 - 28.5)^2 + (55.0 - 20.0)^2 + (51.2 - 46.0)^2 + (38.6 - 34.0)^2 + (43.2 - 36.5)^2 + (48.8 - 52.5)^2 + (25.6 - 26.5)^2 + (49.6 - 46.5)^2) / 7] = 10.87

Calculating the test statistic:

t = (6.85 - 0) / (10.87 / √8) = 2.89

Make a decision

Since the test statistic (2.89) is less than the critical value (2.998), we fail to reject the null hypothesis.

The correct choice is option d. Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

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Question:-

Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an abraded condition. Use the paired t test to test H0: ?D = 0 versus Ha: ?D > 0 at significance level 0.01. (Use ?D = ?U ? ?A.)
State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to three decimal places.)

t ? _______

t ? ________

Compute the test statistic value. (Round your answer to three decimal places.)

t = _____

State the conclusion in the problem context.

a.Reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions.Fail to b.reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions. c.Reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

d.Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions

Answer:

Step 2

Step-by-step explanation:

The quadratic formula is given by [tex]x=-b+-\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]

Our equation is y = 2x²-x-6

So here our a = 2, b = -1, and c = -6

We can now plug these numbers into our formula

[tex]x= -(-1) +-\frac{\sqrt{(-1)^{2}-4(2)(-6) } }{2(2)} = 1 +-\frac{\sqrt{1+24} }{4} = 1+-\frac{\sqrt{25} }{4}[/tex]

Step 2 is incorrect because it states that "x equals the negative of negative 1 plus or minus the square root of negative one plus forty-eight all over two times 2."

The correct statement would be "x equals the negative of negative 1 plus or minus the square root of positive one plus forty-eight all over two times 2.", because the square of a negative is positive, resulting in a positive one.

Since this step is incorrect, the steps after are also incorrect, but Harry went wrong at Step 2

Answer:

The above answer is correct.

Step-by-step explanation:

I got it right on the test

Answer:

6.94% probability that fewer than 35 use self-directed work teams as a management tool

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 70, p = 0.58[/tex]

So

[tex]\mu = E(X) = np = 70*0.58 = 40.6[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{70*0.58*0.42} = 4.13[/tex]

What is the probability that fewer than 35 use self-directed work teams as a management tool?

Using continuity correction, this is P(X < 35 - 0.5) = P(X < 34.5), which is the pvalue of Z when X = 34.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{34.5 - 40.6}{4.13}[/tex]

[tex]Z = -1.48[/tex]

[tex]Z = -1.48[/tex] has a pvalue of 0.0694.

6.94% probability that fewer than 35 use self-directed work teams as a management tool

The question requires calculation of binomial probability. Given that the rate of success is 58% (or 0.58) and we're trying to find the likelihood of fewer than 35 successes out of 70 trials, one must sum the binomial probabilities from k=0 to 34.

This problem is about calculation of binomial probability, which is a specific type of probability that deals with experiments that have two possible outcomes: success (in this case, using self-directed work teams) or failure (not using self-directed work teams). Given that the rate of success is 58% (or 0.58 as a decimal), and we're looking for the probability of fewer than 35 successes out of 70 trials (or managers), we can solve using the formula for binomial probability.

The basic form of the binomial formula is: [tex]P(X=k) = C(n, k) * (p^k) * ((1-p)^{(n-k)})[/tex], where n is the number of trials, k is the number of successful trials, p is the probability of success, and C(n, k) is a combination which calculates the number of possible combinations of n items taken k at a time.

To find P(X<35), we sum from k=0 to 34. Thus, this involves a fair amount of calculation, and you may want to use software or a calculator that has binomial probability functionality.

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Answer: =x2+7x+5

Step-by-step explanation:

−3x2+2x−4+4x2+5x+9

=−3x2+2x+−4+4x2+5x+9

Combine Like Terms:

=−3x2+2x+−4+4x2+5x+9

=(−3x2+4x2)+(2x+5x)+(−4+9)

=x2+7x+5

Answer:

=x2+7x+5

Answer:

x^2+7x+5

Step-by-step explanation:

Remove parentheses: -3x^2+2x-4+4x^2+5x+9

Group like terms: -3x^2+4x^2+2x+5x-4+9

Add similar elements: x^2+2x+5x-4+9

Add/subtract the numbers: x^2+7x+5

Answer:

Step-by-step explanation:

Let the subscripts d and n represent day and night respectively

The null hypothesis is

H0 : μd ≥ μn

The alternative hypothesis is

H1 : μd < μn

it is a one-tailed and also a right left test because of the greater than symbol in the alternative hypothesis.

The decision rule is to reject H0: μd ≥ μn If 0.10 > p value

Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)

z = (xd - xn)/√σd²/nd + σn²/nn

Where

xd and xn represents sample means for day and night respectively.

σd and σn represents population standard deviations for day and night respectively.

nd and nn represents number of samples

From the information given,

xd = 334

xn = 341

σd = 23

σ2 = 28

nd = 60

nn = 68

z = (334 - 341)/√23²/60 + 28²/68

= - 7/√20.34607843138

z = - 1.55

From the normal distribution table, the probability value corresponding to the z score is 0.061

Since the level of significance, 0.1 > 0.061, we would reject H0

Therefore, there is enough evidence to conclude that there are more units produced on the night shift than on the day shift.

Final answer:

Clark Heter is conducting a one-tailed test to compare the mean production of day and night shifts. The decision to reject the null hypothesis that day shift production is greater or equal to night shift production is based on a critical value of -1.28 linked to a significance level of 0.10. The test statistic is computed from the given means and standard deviations for both samples.

Explanation:

Conducting a Two-Sample Z-Test

Clark Heter wants to determine if more units are produced on the night shift than on the day shift. Given the samples:
- Day-shift (n=60): mean = 334, population standard deviation = 23.
- Night-shift (n=68): mean = 341, population standard deviation = 28.
The significance level is 0.10.

Answer:

t = 17.5°

f = 12°

Step-by-step explanation:

MNOP is a square  and the angle M is (4t + 20)° and the angle N is (7f + 6)°. The value of t and f can be calculated below.

A square is a quadrilateral and all the sides are equal. Opposite sides are parallel to each other . Each angle of a square is equal to 90°.  

Since ∠M = 4t + 20

This means ∠M

4t + 20 = 90

4t = 90 - 20

4t = 70

t = 70/4

t = 17.5°

∠N = 7 f + 6

7 f + 6 = 90

7f = 90 -6

7f = 84

f = 84/7

f = 12°

Answer:

t=17.5

f=12

Step-by-step explanation:

Answer:

6/25 probability

Step-by-step explanation:

We have 5 marbles total,   3 + 2  = 5

Find P(  white marble, yellow marble with replacement)

= P(white, yellow) = (2/5)*(3/5) =  6 / 25

Answer:

8000

Step-by-step explanation:

1/4 of 16000 is 4000

16000-4000=12000 1/3 of 12000 is also 4000

12000-4000=8000

Answer:

A, B, and D.

Step-by-step explanation:

The absolute value function is V shaped, goes through the origin, and never dips below the x axis, meaning that it is in the 1st and 2nd quadrants. The left side resembles a line with slope -1, which means that choice C is incorrect. Hope this helps!

Answer:

Proposal B

Step-by-step explanation:

This problem can be solved by comparing the expected returns on both options.

The expected return is the sum of the possible outcomes multiplied by its probabilities of occurrence.

For proposal A, the net profits are $20,000, $30,000 and $50,000, with respective probabilities 0.2, 0.4 and 0.4. Then, the expected return can be calculated as:

[tex]E(A)=\sum_{i=1}^3p_iR_i\\\\E(A)=p_1R_1+p_2R_2+p_3R_3\\\\E(A)=0.2*20,000+0.4*30,000+0.4*50,000\\\\E(A)=4,000+12,000+20,000\\\\E(A)=36,000[/tex]

The proposal A has a expected net profit of $36,000.

The proposal B has a 50% chance of having a net profit of $100,000 and a 50% of break even (zero net profit). We applied the same calculation for the expected profit and we have:

[tex]E(B)=\sum_{i=1}^2p_iR_i\\\\E(B)=p_1R_1+p_2R_2\\\\E(B)=0.5*100,000+0.5*0\\\\E(B)=50,000[/tex]

The proposal B has a expected net profit of $50,000.

Assuming that each proposal requires the same investment, the proposal B has more expected monetary return (GHȼ 50,000) than proposal A (GHȼ 36,000).

Answer: 1007.28

Step-by-step explanation:

Given : The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with

[tex]\mu=820\ \ \ ,\ \sigma=200[/tex]

If a college requires a student to be in the top 15 % of students taking this test, it means that they want the students that score 85 percentile or above.

Let X be the scores of any random student, we require

[tex]P(X<x)=0.85[/tex], where x is minimum score that such a student can obtain and still qualify for admission at the college.

Formula for z-score = [tex]z=\frac{x-\mu}{\sigma}=\frac{x-820}{200}[/tex]  ...(i)

From normal z-value table , [tex]P(z<1.036)=0.85[/tex]...(ii)

From (i) and (ii) , we get

[tex]\frac{x-820}{200}=1.0364\\\\\Rightarrow\ x-820=207.28\\\\\Rightarrow\ x=207.28+820=1007.28[/tex]

Hence, the minimum score that such a student can obtain and still qualify for admission at the college is 1007.28.

The combined weight of the two kittens is 70 ounces.

To find the combined weight of the two kittens, we'll start by converting the weight of the first kitten to ounces.

1 pound is equal to 16 ounces, so 2 pounds is equal to 2 x 16 = 32 ounces.

Therefore, the first kitten weighs 32 + 4 = 36 ounces.

The weight of the second kitten is 2 ounces less, so we subtract 2 from the weight of the first kitten: 36 - 2 = 34 ounces.

Finally, we can find the combined weight by adding the weights of the two kittens together: 36 + 34 = 70 ounces.

Therefore, the combined weight of the two kittens is 70 ounces.

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Answer:

B. 104

Step-by-step explanation:

Just find the area of the wall and subtract the area of the window. The area of the wall is 10 times 11 which is 110. The area of the window is 2 times 3 which is 6. 110 minus 6 is 104.

There are 32,760 ways to select 4 winners from 15 participants in a local raffle where the order of prizes matters according to permutation.

To find out how many ways 4 winners can be selected from 15 participants in a local raffle with given prizes, we can use the concept of permutation because the order in which the prizes are awarded matters (i.e., the prizes are not identical).

The total number of different ways to select 4 winners from 15 participants is represented by the permutation of 15 things taken 4 at a time (since the order of selection matters for different prizes).

The formula for permutation is: P(n, k) = n! / (n-k)! where n is the total number of items, k is the number of items to choose, and '!' represents a factorial.

For this problem, we calculate P(15, 4):

Therefore, there are 32,760 ways to select 4 winners from 15 participants.

Answer: $$$99.36

Step-by-step explanation:

It's 11.04 for 2 stamps

U have to buy 18 stamps

18÷2=9

9×11.04=99.36

Answer:

It costs $5.52 to Sam to buy 12 stamps.now multiply

Step-by-step explanation:

Answer:

120.

Step-by-step explanation:

This is the number of combinations of 3 from 10.

This = 10C3

= 10! / 3! (10-3)!

= 10*9*8 / 3*2*1

= 120 combinations.

Answer:

120

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

After performing the calculations, the right matrix multiplication by D changes each column of A and the left matrix multiplication by D changes each row of A. Also, there are an infinite number of 3x3 matrices that satisfy the condition AB ≠ BA

To compute the products AD and DA, we first need to understand how matrix multiplication works. Given matrices A and D as presented, it is important to understand that when A is multiplied by D on the right side (AD), each column of A is multiplied by the corresponding diagonal entry of D. Conversely, when A is multiplied by D on the left side (DA), each row of A is multiplied by the corresponding diagonal entry of D. This is true for any two matrices you want to multiply. Therefore, the correct answer to the first part of the question is statement D.

For the second part of the question, we're seeking a non-identity, non-zero 3x3 matrix B such that AB is not equal to BA. This is generally quite difficult and requires some trial and error. There are an infinite number of matrices B that satisfy the condition AB ≠ BA. The exact form of B depends on A and can be quite complex, but B isn't necessarily unique. Therefore, the correct answer to this question is B: There are infinitely many solutions.

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Answer:

4 / 9  probability of getting a red

Step-by-step explanation:

How many marbles are there total?

4 red + 2 yellow + 3 green = 9 marbles total

P( red marble) = 4 red / 9 total = 4/9

Answer:

Step-by-step explanation:

Red marbles- 4

Yellow marbles-2

Green marbles-3

Total marbles=9

Probability= 4/9

=0.4444

Answer:

We conclude that the mean time taken to finish undergraduate degrees is longer than 4.5 years.

Step-by-step explanation:

We are given that an article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees.

You conduct a survey of 39 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2.

Let [tex]\mu[/tex] = average time taken to finish their undergraduate degrees.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 4.5 years     {means that the mean time taken to finish undergraduate degrees is equal to 4.5 years}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 4.5 years     {means that the mean time taken to finish undergraduate degrees is longer than 4.5 years}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                           T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean time = 5.1 years

            s = sample standard deviation = 1.2 years

            n = sample of students = 39

So, the test statistics  =  [tex]\frac{5.1-4.5}{\frac{1.2}{\sqrt{39} } }[/tex]  ~ [tex]t_3_8[/tex]

                                     =  3.122

The value of t test statistics is 3.122.

Now, at 1% significance level the t table gives critical value of 2.429 at 38 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 3.122 > 2.429, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean time taken to finish undergraduate degrees is longer than 4.5 years.

Answer:

[tex]t=\frac{27.1-27.4}{\frac{7.3}{\sqrt{4934}}}=-2.887[/tex]    

The degrees of freedom are given by:

[tex] df= n-1 = 4934-1= 4933[/tex]

Then the p value for this case calculated as:

[tex]p_v =P(t_{4933}<-2.887) =0.002[/tex]  

Since the p value is a very lower value using any significance level for example 1% or 5% we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significanctly less than 27.4. So then is not anything wrong with the conclusion

Step-by-step explanation:

Information provided

[tex]\bar X=27.1[/tex] represent the sample mean

[tex]s=7.3[/tex] represent the sample standard deviation

[tex]n=4934[/tex] sample size  

[tex]\mu_o =27.4[/tex] represent the value to test

t would represent the statistic  

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if the mean age of​ full-time students did decline (less than 27.4), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 27.4[/tex]  

Alternative hypothesis:[tex]\mu < 27.4[/tex]  

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{27.1-27.4}{\frac{7.3}{\sqrt{4934}}}=-2.887[/tex]    

The degrees of freedom are given by:

[tex] df= n-1 = 4934-1= 4933[/tex]

Then the p value for this case calculated as:

[tex]p_v =P(t_{4933}<-2.887) =0.002[/tex]  

Since the p value is a very lower value using any significance level for example 1% or 5% we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significanctly less than 27.4. So then is not anything wrong with the conclusion