Question

Jeffrey is as an eight-year old, who used to believe that his mean time for swimming the 25-

yard freestyle was 16.43 seconds. Jeffrey’s dad, Frank, thought that Jeffrey could swim the 25-

yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and

timed Jeffrey for 15 25-yard freestyle swims. For the 15 swims, Jeffrey's mean time was 16

seconds with a standard deviation of 0.8 seconds. Frank thought that the goggles helped Jeffrey

to swim faster than the 16.43 seconds

.

a) Conduct a hypothesis test using α = 0.05. Assume that the swim times for the 25-yard freestyle

are normal.

b) Conduct a hypothesis test using α = 0.01. Assume that the swim times for the 25-yard

freestyle are normal.

Answer 1

As we are testing here whether the mean is less than 16.43 seconds, therefore the null and the alternate hypothesis here are given as:

Ho :μ = 16.43

H, :μ< 16.43

The test statistic here is computed as:

r - – ཅn – 16 – [t. 43 – -20817

For n - 1 = 14 degrees of freedom, we get the p-value from the t distribution tables as:

p = P( t₁₄ < -2.0817) = 0.0281

a) As the p-value here is 0.0281 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here and conclude that we have sufficient evidence that goggles helped Jeffrey to swim faster than the 16.43 seconds.

b) As the p-value here is 0.0281 > 0.01 which is the level of significance here, therefore we the test is not significant here and we dont have sufficient evidence here that that goggles helped Jeffrey to swim faster than the 16.43 seconds.