A consumer researcher was asked to test a claim by a franchise swimming instruct

Question

A consumer researcher was asked to test a claim by a franchise swimming instruction program. Specifically, they claimed that they could teach the average 7-year-old to swim across an Olympic-size pool in less than 2 hours. The researcher arranged for eight randomly selected 7-year-old children to take instruction at this school and kept a careful record of how long it took each child. The times (in minutes) were 60, 120, 110, 80, 70, 90, 100, and 130. What should the researcher conclude? Carry out a t test for a single sample (120 minutes is the known population mean) using the .01 significance level.

a. what type of statistical test should be conducted on this data and why ?

b. conduct the five steps of hypothesis testing?

c. figure the effect size, is this small medium or large effect?

Explanation / Answer

Set Up Hypothesis
Null, H0: U=120
Alternate, H1: U<120
Test Statistic
Population Mean(U)=120
Sample X(Mean)=95
Standard Deviation(S.D)=24.4949
Number (n)=8
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =95-120/(24.4949/Sqrt(8))
to =-2.887
| to | =2.887
Critical Value
The Value of |t | with n-1 = 7 d.f is 2.998
We got |to| =2.887 & | t | =2.998
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -2.8868 ) = 0.01171
Hence Value of P0.01 < 0.01171,Here We Do not Reject Ho

[ANSWERS]
a. Left tailed test
b. Small

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