Question

According to a Pew Research Center study, in May 2011, 40% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 341 community college students at random and finds that 147 of them have a smart phone. Then in testing the hypotheses:

H0: p = 0.4 versus

Ha: p > 0.4,

what is the test statistic?

z =________________. (Please round your answer to two decimal places.)

B.)

According to a Pew Research Center study, in May 2011, 33% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 349 community college students at random and finds that 138 of them have a smart phone. In testing the hypotheses:

H0: p = 0.33 versus

Ha: p > 0.33,

she calculates the test statistic as z = 2.5990.

Then the p‑value =________________ .

(Please round your answer to four decimal places.)

Answer 1

z = 1.17

P - value = 0.0047

Explanation:

A.

From the given information;

H0: p = 0.4 versus

Ha: p > 0.4,

Let's calculate the population proportion for the point estimate;

the population proportion
`\hat p` = 147/341

the population proportion
`\hat p` = 0.431085

However; the test statistics can therefore be determined by using the formula:

`z = \frac{\hat p - p_o}{\sqrt{(p_o(1-p_o))/(n)}}`

`z = \frac{0.431085 - 0.40}{\sqrt{(0.40(1-0.40))/(341)}}`

`z = \frac{0.031085}{\sqrt{(0.40(0.60))/(341)}}`

`z = \frac{0.031085}{\sqrt{(0.24)/(341)}}`

`z = \frac{0.031085}{\sqrt{7.03812317 * 10^(-4)}}`

`z = (0.031085)/(0.0265294613)`

z = 1.1717

z = 1.17 to two decimal places

B.)

The null and the alternative hypothesis is given as:

H0: p = 0.33 versus

Ha: p > 0.33,

The z = 2.5990.

The objective here is to determine the p-value from the z test statistics.

P - value = P(Z > 2.5990)

P- value = 1 - P(Z < 2.5990)

P - value = 1 - 0.9953

P - value = 0.0047