A survey reported the number of meters (m) per week swam by two groups of swimmers—those who competed exclusively in breaststroke and those who competed in the individual medley (which includes breaststroke). The number of meters per week practicing the breaststroke was recorded for each swimmer, and the summary statistics are given below. Is there sufficient evidence to indicate that the average number of meters per week spent practicing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley?

Complete Question:

A survey reported the number of meters (m) per week swam by two groups of swimmers—those who competed exclusively in breaststroke and those who competed in the individual medley (which includes breaststroke). The number of meters per week practicing the breaststroke was recorded for each swimmer, and the summary statistics are given below. Is there sufficient evidence to indicate that the average number of meters per week spent practicing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley?

                                                                               Specialty            

                                                Exclusive Breaststroke        Individual Medley

Sample size                                             130                                        80

Sample mean (m)                                    9017                                      5853

Sample standard deviation (m)              7162                                       1961

Population mean                                                                               

a. State the null and alternative hypothesis

b. What is the appropriate rejection region for an α = 0.01 level test?

c. Calculate the observed value of the appropriate test statistics

d. What is your conclusion?

e. What is a practical reason for the conclusion you reached in pat (d)?

c. 4.76

Explanation:

from the table shown above

let Y₁ be the number of meters (m) per week swum by those who competed exclusively in the Beast stroke

let Y₂ be the number of meters per week swum by those who competed in the individual medley

a)

Null hypothesis H₀:

alternative Hypothesis H₁:    (Right tailed test)

the attached images shows additional details of the solution

Yes

Explanation:

The data for both groups is missing in the question. It is shown in the attachment.

The data mentions sample size, mean and standard deviations of both the samples. This data can be used to test the hypothesis that "average number of meters per week spent practicing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley".

Using the data, t-value, p-value and critical values can be determined

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