Question

Many students brag that they have more than 125 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 125​?

110 40 250 20 250 225 270 180 175 225 130 35 175

b. State the null and alternative hypotheses.

c. Find and interpret the test statistic value. t equals 1.53 ​(Round to two decimal places as​ needed.)

What does the test statistic value​ represent?

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

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

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

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

d. Report and interpret the​ P-value and state the conclusion in context. Use a significance level of 0.05.

The​ P-value is . 3685. ​(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 the null hypothesis being true.

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

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

e. Complete the phrase

Since the​ P-value is

a.greater

b.less than

the level of​ significance, the sample

a.does

b.does not

provide evidence to reject the null hypothesis. There is

A. sufficient

B.insufficient

evidence to conclude that the mean number of friends on the social media website is larger than 125.

Answer 1

(b). Hypothesis

$H_{0}:\mu =125$ vs $H_{1}:\mu > 125$

(c). Test statistics: tcal$=1.47$ and critical value tc$=1.78$

Here test statistic is less than the critical value so we accept null hypothesis H0.

The test statistic value​ represents:

(B). The test statistic value is the difference between the sample mean and the null hypothesis value.

(d). P-value$=0.084$ and level of significance,
= 0,05

Here P-value is greater than level of significance so we conclude that the mean number of friends for the student population at the college who use the social media website is not larger than 125​.

The​ P-value represents:

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

(e). Since P-value is (a) greater than the level of significance, the sample (b) does not provide evidence to reject the null hypothesis. There is (B) insufficient evidence to conclude that the mean number of friends on the social media website is larger than 125.