Question

A sample of 100 students from 9th grades at AA High School can do an average of 11.5 pull-ups (chin-ups) in 30 seconds, with standard deviation of 3.162. The US Department of Health and Human Services suggests 9th grades should do a minimum of 9 pull-ups in 30 seconds. Are the 9th graders at AA High School able to do significantly more pull-ups than the number recommended by the US Department of Health and Human Services? Using this information, answer the following: a) Expressed in terms of μ, what are the null and alternate hypotheses? b) Calculate the standard error of the mean. c) Determine a 90% confidence interval for the mean. d) What is the observed test-statistic value? e) What is the p-value for this test statistic? f) Using significance level of .05, what decisions should you make about the null and alternate hypotheses? What should you conclude about the pull-up minimum?

Answer 1

n=100, xbar= 11.5 pull ups , standard deviation= 3.162 pull ups.

NULL HYPOTHESIS H0: PULL UPS

ALTERNATIVE HYPOTHESIS HA: PULL UPS

b) standard error of means =

=

Standard error =

c) 90% confidence interval is

t critical = 1.66
sM = √(3.162^2/100) = 0.32

μ = M ± t(sM)
μ = 11.5 ± 1.66*0.32
μ = 11.5 ± 0.525

CI [10.975, 12.025].

You can be 90% confident that the population mean (μ) falls between 10.975 and 12.025.

d) observed test statistic value

e) P value=3.73 E-12

f) Since P value is smaller than 0.05 we reject null hypothesis H0. We have sufficient evidence to show that the 9th graders at AA High School able to do significantly more pull-ups than the number recommended by the US Department of Health and Human Services.