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Consider the following hypothesis test. H0: μ ≥ 55 Ha: μ < 55 A sample of 36 is used. Identify the p-value and state your con

Ket [755]

Answer:

Step-by-step explanation:

Given that:

$H_o: \mu \ge 55 \ \\ \\ H_1 : \mu < 55$

(a) For x = 54 and s = 5.3

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{54-55}{\dfrac{5.3}{\sqrt{36}} }$

$Z = \dfrac{-1}{\dfrac{5.3}{6} }$

Z = -1.132

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-1.132,35,1) = 0.1326

Decision: p-value is greater than significance level; do not reject $\mathbf{H_o}$

$Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \$ $\mu < 55$

b

For x = 53 and s = 4.6

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{53-55}{\dfrac{4.6}{\sqrt{36}} }$

$Z = \dfrac{-2}{\dfrac{4.6}{6} }$

Z = -2.6087

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-2.6087,35,1) =0.0066

Decision: p-value is < significance level; we reject the null hypothesis.

$Conclusion: \ There \ is \ sufficient \ evidence \ to \ conclude \ that$ $\mu < 55$

c)

For x = 56 and s = 5.0

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }$

Z = 1.2

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(1.2,35,1) = 0.88009

Decision: p-value is greater than significance level; do not reject $\mathbf{H_o}$

$Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \$ $\mu < 55$

6 0

3 years ago

The woods family traveled 25 miles in 1/2 hour. If it is currently 3:00 pm and the family's destination is 225 miles away at wha

svetlana [45]

<span>Given: family travelled 25 miles in 30 minutes or 50 miles /hr current time 3.00 pm. total distance=225 miles. solution: speed = distance * time time = distance/spedd = 225/50 time = 4.5 hours. reaching time= 3 hours +4 hour 30 minutes= 7.30 pm</span>

5 0

3 years ago

What is the difference between the following two regression equations? Choose the correct answer below.

olga55 [171]

Answer:

The correct option is (A). The first equation is for sample data; the second equation is for a population.

Step-by-step explanation:

According to the scenario, the following would be represented as a sample and the population

Y with caret = b0 + b1x = sample

and

y = b0 + b1x = population

It is because if we considered the population than the expected value would be nearest and there is no need to determine the b0 and b1 value again. But in the case of the sample, the reestimation of the values would be determined again and again

Therefore the correct option is A.

8 0

3 years ago

Can you subtract closed polynomials

netineya [11]

Answer:

Polynomials are closed under addition. When subtracting polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the difference has variables and exponents which are already classified as belonging to polynomials.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

At the bake sale there were 40 raisin cookies sold. If ratio of raisin cookies sold to oatmeal cookies sold was 5:1 what is the

Annette [7]

Answer:

48 cookies were sold in total.

Step-by-step explanation:

5:1 is the ratio of raisin cookies to oatmeal cookies, and 40 raisin cookies were sold. Meaning, 40:?.

To find the number of oatmeal cookies you divide 40 by 5, which gets 8. This means that the original ratio is multiplied by 8 to get the current ratio for the amount if cookies. 5(8) : 1(8) = 40:8. There are 40 raisin cookies and 8 oatmeal cookies. 40+8=48. There were 48 cookies sold in total.

6 0

3 years ago