Question

Many students brag that they have more than 150 friends on a social media website. For a class​ project, a group of students asked a random sample of 13 students at their college who used the social media website about their number of friends and got the data available below. Is there strong evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150​?

data: 125 50 105 120 210 200 200 200 100 185 255 250 235

Complete parts a through d below.

a. Identify the relevant variable and parameter.What is the relevant​ variable?

What is the​ parameter?

b. State the null and alternative hypotheses.

c. Find and interpret the test statistic value.​(Round to two decimal places as​ needed.)

What does the test statistic value​ represent?

A.The test statistic value is the number of standard errors from the null hypothesis value to the sample mean.

B.The test statistic value is the number of standard deviations from the null hypothesis value to the sample mean.

C.The test statistic value is the difference between the sample mean and the null hypothesis value.

D.The test statistic value is the expected mean of the differences between the sample data and the null hypothesis value.

d. Report and interpret the​ P-value and state the conclusion in context. Use a significance level of 0.05​(Round to three decimal places as​ needed.)

What does the​ P-value represent?

A.The​ P-value is the probability of observing a sample mean this high or higher if the null hypothesis is true.

B.The​ P-value is the probability of observing this value for the sample mean if the null hypothesis is true.

C.The​ P-value is the probability of observing a sample mean this low or lower if the null hypothesis is true.

D.The​ P-value is the probability of the null hypothesis being true.

Since the​ P-value is ----- than the level of​ significance, the sample ------ provide evidence to reject the null hypothesis. There is ------ evidence to conclude that the mean number of friends on the social media website is larger than 150.

Answer 1

(a)

the relevant​ variable : number of friends for the student population at the college who use the social media website

the​ parameter : the mean number of friends for the student population at the college who use the social media website

(b)

H0: Null Hypothesis: 150 ( The mean number of friends for the student population at the college who use the social media website is not larger than 150​ )

HA: Alternative Hypothesis: 150 ( The mean number of friends for the student population at the college who use the social media website is larger than 150​ ) (Claim)

(c)

From the given data, the following statistics are calculated:

n = 13

= 171.9231

s = 64.7926

= 0.05

Test Statistic is given by:

Test Statistic = 1.22

Correct option:

A.The test statistic value is the number of standard errors from the null hypothesis value to the sample mean.

(d)

By Technology,

p - value = 0.1230

Correct option:

C.The​ P-value is the probability of observing a sample mean this low or lower if the null hypothesis is true.

(e)

Since the​ P-value is greater than the level of​ significance, the sample does not provide evidence to reject the null hypothesis. There is is not suffcient- evidence to conclude that the mean number of friends on the social media website is larger than 150.