A survey of 900 adults from a certain region? asked, "What do you buy from your mobile? device?" The results indicated that 49?% of the females and 42?% of the males answered clothes

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A survey of 900 adults from a certain region? asked, "What do you buy from your mobile? device?" The results indicated that 49?% of the females and 42?% of the males answered clothes. The sample sizes of males and females were not provided. Suppose that of 300 ?females, 147 reported they buy clothing from their mobile? device, while of 600 ?males, 252 reported they buy clothing from their mobile device. Complete parts? (a) through? (d) below.

a. Is there evidence of a difference between males and females in the proportion who said they buy clothing from their mobile device at the 0.1 level of? significance?

State the null and alternative? hypotheses, where π1 is the population proportion of females who said they buy clothing from their mobile device and π2 is the population proportion of males who said they buy clothing from their mobile device.

A.

H0?: π1=π2

H1?: π1>π2

B.

H0?: π1≠π2

H1?: π1=π2

C.

H0?: π1≠π2

H1?: π1>π2

D.

H0?: π1=π2

H1?: π1<π2

E.

H0?: π1=π2

H1?: π1≠π2

Your answer is correct.

F.

H0?: π1≠π2

H1?: π1<π2

Determine the value of the test statistic.

ZSTAT=

1.99

 

1.99 ?(use an integer or a decimal. Round to two decimal places as? needed.)

Determine the critical? value(s) for this test of hypothesis.

The critical? value(s) is? (are)

negative 1.64 comma 1.64

 

−1.64,1.64.

?(Type integers or decimals. Round to two decimal places as needed. Use a comma to separate answers as? needed.)

State the conclusion.

Reject

the null hypothesis. There is sufficient

evidence to support the claim that there is a difference between males and females in the proportion who said they buy clothing from their mobile device

b. Find the? p-value in? (a) and interpret its meaning.

The? p-value in part? (a) is

0.046

 

0.046.

?(use an integer or a decimal. Round to three decimal places as? needed.)

What does the? p-value mean?

A.

The? p-value is the probability that the null hypothesis is true.

B.

The? p-value is the probability of obtaining a result at least as extreme as the one obtained with this sample given that the null hypothesis is true.

Your answer is correct.

C.

The? p-value is the probability of rejecting the null hypothesis if the test were repeated for different samples.

D.

The? p-value is the probability of falsely rejecting the null hypothesis.

c. Construct and interpret a 90?% confidence interval estimate for the difference between the proportion of males and females who said they buy clothing from their mobile device.

The confidence interval is

0.0121

 

0.0121 to

0.1279

 

0.1279.

?(Type integers or decimals. Round to four decimal places as needed. Use ascending? order.)

What does the confidence interval? mean?

A researcher can be 90%

confident that the difference in the population proportions of males and females who said they buy clothing from their device is contained in

the interval.

d. What are your answers to? (a) through? (c) if 264 males said they buy clothing from their mobile? device?

Is there evidence of a difference between males and females in the proportion who said they buy clothing from their mobile device at the 0.1 level of? significance? State the null and alternative? hypotheses, where π1 is the population proportion of females who said they buy clothing from their mobile device and π2 is the population proportion of males who said they buy clothing from their mobile device.

A.

H0?: π1=π2

H1?: π1≠π2

Your answer is correct.

B.

H0?: π1≠π2

H1?: π1=π2

C.

H0?: π1≠π2

H1?: π1<π2

D.

H0?: π1=π2

H1?: π1<π2

E.

H0?: π1≠π2

H1?: π1>π2

F.

H0?: π1=π2

H1?: π1>π2

 

Determine the value of the test statistic.

ZSTAT=