Question

A shoe manufacturer claims that athletes can increase their vertical jumps using the manufacturer’s training shoes. The vertical jump heights of 8 randomly selected athletes are measured before they tried they shoes and then after they had been wearing the shoes for 9 months. The heights in inches are shown below. Assume vertical jump heights are normally distributed. Let and .

Athlete	1	2	3	4	5	6	7	8
Vertical Jump Height (before using shoes)	24	22	25	28	35	32	30	27
Vertical Jump Height (after using shoes)	26	25	25	29	33	34	35	30

Write the hypotheses for this test.

Using your hypotheses, determine which tailed test this is.

Calculate the value of the standardized test statistic. Round your answer to 2 decimal places.

Calculate the P-Value for this test statistic. Round your answer to 4 decimal places

Based on this P-Value, what decision should you make?

Either the test resulted in an error or a correct decision. If an error was made, what type of error was it?

please show work/ excel work

Answer 1

(a)

Question:

Write the hypotheses for this test.

H0:Null Hypothesis: 0 ( Athletes cannot increase their vertical jumps using the manufacturer’s training shoes. )

HA: Alternative Hypothesis: 0 ( Athletes can increase their vertical jumps using the manufacturer’s training shoes. ) (Claim)

(b)

Question:

Using your hypotheses, determine which tailed test this is.

Answer:
This is Left Tailed test

(c)

Question:

Calculate the value of the standardized test statistic. Round your answer to 2 decimal places.

From the given data, values of d = Athlete vertical jump height (before using shoes) - Athlete vertical jump height (after using shoes)are calculated as follows:

d = Athlete vertical jump height (before using shoes) - Athlete vertical jump height (after using shoes) = -2,-3,0,-1,2,-2,-5,-3

From d values, the following statistics are calculated:

n = 8

= - 1.75

s_d = 2.121

Test Statistic is given by:

(d)

Question:

Calculate the P-Value for this test statistic. Round your answer to 4 decimal places

By Technology,

p - value = 0.0262

(e)

Question:

Based on this P-Value, what decision should you make?

Answer:
Since is notgiven, take = 0.05

Since p - value = 0.0262 is less than = 0.05, the difference is significant. Reject null hypothesis.

The data support the claim that athletes can increase their vertical jumps using the manufacturer’s training shoes.

(f)

Question:

Either the test resulted in an error or a correct decision. If an error was made, what type of error was it?

If an error was made, it was Type I Error: Rejection of a true null hypothesis, because we have rejected the null hypothesis.