Question

a hypothesis test claims that Americans enjoy podcasts that are 25 minutes long on average. The results of a one-sample test for the preferred average length of a podcast is given in the following output. Test at the α = 0.05 significance level

sample T summary hypothesis test:

u = mean of population

H₀: u = 25

H_A:u not equal to 25

hypothesis test results

mean= u

sample mean=25.4

std. err= 0.21902066

DF= 1802

T-stat = 1.8263117

p-value = 0.068

a. Does the output show that your should reject the null hypothesis or fail to reject the null hypothesis? Why?

b. Is the null hypothesis the same statement as the original claim or different?

c. Write a formal conclusion addressing the original context

Answer 1

Given that,

A hypothesis test claims that Americans enjoy podcasts that are 25 minutes long on average. The results of a one-sample test for the preferred average length of a podcast is given in the following output. Test at the significance level.

sample T summary hypothesis test:

u = mean of population

H0: u = 25

HA:u not equal to 25

hypothesis test results

mean= u

sample mean=25.4

std. err= 0.21902066

DF= 1802

T-stat = 1.8263117

p-value = 0.068

a)

Now we want to check does the output show that we should reject the null hypothesis or fail to reject the null hypothesis.

Rejection Rule:

We reject the null hypothesis at level if we get, p-value

Here from the output we get, p-value = 0.068

i.e. we get p-value = 0.068

Result: Fail to reject the null hypothesis.

Answer: Fail to reject the null hypothesis. Since we get p-value is greater than significance level

b)

Here given that, a  hypothesis test claims that Americans enjoy podcasts that are 25 minutes long on average.

And null hypothesis is given by, H0: u = 25

[ Where u = Population mean ]

i.e. we get null hypothesis is same statement as the original claim.

Answer: null hypothesis is same statement as the original claim.

c)

Now we write the conclusion about the original claim.

Conclusion: From the above testing result at level we can conclude that the claim Americans enjoy podcasts that are 25 minutes long on average are correct/true.