In 2016, Americans express a clear preference for getting their news on a screen

Question

In 2016, Americans express a clear preference for getting their news on a screen, although which screen that is varies. Television (TV) remains the dominant screen, with 69% of all U.S. adults getting news through this platform. Is this rate higher for U.S. adults aged 65 and older? A random sample of 22 U.S. adults aged 65 and older was taken, and 21 of the sampled adults reported getting their news by watching TV. Use a 1% significance level.

Question 7 Subquestions

7.a

1 point(s)

The hypotheses to be tested are H0: p = 0.69 versus Ha: p > 0.69. Clearly define the parameter p in the context of the problem.

No answer entered. Click above to enter an answer.

7.b

1 point(s)

If the null hypothesis is true, what is the distribution of the test statistic (that is, which distibution should be used to find the p-value)?

N(0,1) distribution

N(15.18, 2.1693) distribution

Bin(n = 22, p = 0.9545) distribution

Bin(n = 22, p = 0.69) distribution

7.c

1 point(s)

Report the observed value of the test statistic for testing the hypotheses in part (a).

No answer entered. Click above to enter an answer.

7.d

2.5 point(s)

Compute the p-value for this test.

No answer entered. Click above to enter an answer.

7.e

1 point(s)

Our decision at the 1% level of significance is to reject the null hypothesis. Based on our decision, the appropriate conclusion in context is:

(Challenge: before looking at the four options, try writing out the conclusion in context yourself ~ then compare it to the four options ~ good practice.)

There is not sufficient evidence to conclude that the sample proportion of all US adults 65 and older who get their news by watching TV is more than 0.69.

There is not sufficient evidence to conclude that the population proportion of all US adults 65 and older who get their news by watching TV is more than 0.69.

There is sufficient evidence to conclude that the sample proportion of all US adults 65 and older who get their news by watching TV is more than 0.69.

There is sufficient evidence to conclude that the population proportion of all US adults 65 and older who get their news by watching TV is more than 0.69.

7.f

0.5 point(s)

If the study will be repeated in the future with the same sample size selected from the sampled populaton, but now a 5% significance level will be used, then the probability of correctly rejecting the null hypothesis would...

increase

decrease

stay the same

Explanation / Answer

(7a) p=proportion of US-adults=0.69

(7b) test statistics z=(P-p)/SE(p)~N(0,1)

(7c) z=(0.9545-0.69)/0.0986=2.68

P=21/22=0.9545, p=0.69,

SE(p)=sqrt((p(1-p)/n)=sqrt(0.69*(1-0.69)/22)=0.0986

(7d) one-tailed p-value=0.0037 ( using excel commmand=1-=NORMSDIST(2.68)

(7e) since p-value =0.0037 is less than alpha=0.01, so we reject null hypothesis H0

(7f) increase,

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.