1 Historically the average time it takes Jessica to swim the

1. Historically, the average time it takes Jessica to swim the 200 meter butterfly is 148.4 seconds. Jessica would like to know if her average time has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 seconds with a standard deviation of 2.3 seconds. Perform the appropriate test of hypothesis to determine whether Jessicas average time has changed.

A. Ho: xbar=147.8 vs Ha: xbar not equal to 147.8
B. Ho: mu=148.8 vs Ha: mu not equal 148.4
C. Ho: mu=147.8 vs Ha: mu not equal to 147.8
D. Ho: xbar=148.8 vs Ha: xbar not equal to 148.4

2. using the information from question 1, the hypothesis to be tested are Ho mu=148.4 vs Ha: mu not equal to 148.4
What is the test statistic T, round to two decimals?

Solution

Set Up Hypothesis
Null, H0: U=148.4
Alternate, H1: U!=148.4
Test Statistic
Population Mean(U)=148.4
Sample X(Mean)=147.8
Standard Deviation(S.D)=2.3
Number (n)=50
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =147.8-148.4/(2.3/Sqrt(50))
to =-1.845
| to | =1.845
Critical Value
The Value of |t | with n-1 = 49 d.f is 2.01
We got |to| =1.845 & | t | =2.01
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -1.8446 ) = 0.0711
Hence Value of P0.05 < 0.0711,Here We Do not Reject Ho

[ANSWER]
1. B. Ho: mu=148.8 vs Ha: mu not equal 148.4
2. to =-1.85