Question

27.) Use the following information to answer questions 27 & 28:

A statistics teacher wants to see if there is any difference in the performance of students on the final exam if she gives them orange jelly beans before the exam. She has a theory that orange jelly beans will change the results, but she isn't sure in which direction. She knows that the population mean score on the exam when students do not have orange jelly beans is 82 and that exam scores have an approximately symmetric distribution. She gives orange jelly beans to 25 randomly selected students and finds that these students had a sample mean score of 87 with a sample standard deviation of 10. She wants to have 95% confidence in her result.

27.) Conduct a hypothesis test using the p-value approach.

28.) Conduct a hypothesis test using the confidence interval approach.

Answer 1

Given:

x̅=87

s=10

n=25

27.)

Degree of freedom(df)=n-1=25-1=24

Test Statistic(t):

use excel Function  =TDIST(2.5,24,2)

Now, Significance=1-0.95=0.05

here

P-Value<Significance level(alpha=0.05), Reject Null Hypothesis

Hence, There is sufficient evidence to support the claim that the orange jelly beans will change the results,

28.)

Confidence=95%

Degree of freedom=24

Critical value at 95% confidence(t_c)= 2.064 (use T distribution table)

95% confidence Interval:

From the above Confidence interval, we can see that the true population mean do not lie within this confidence Interval.

Hence we can conclude that the orange jelly beans will change the results