A company wants to promote a new product to college students using social media. According to 2020 data, the average Facebook user has about 300 friends, and Facebook is the most popular social network among college students. The company has decided to start an advertising campaign if they get conclusive evidence that the average number of Facebook friends among college students is over 300. The company randomly selected a sample of 51 Ontario college students. For this sample group, the mean is 306 and the standard deviation is 34. Suppose that the distribution of number of Facebook friends is symmetric and approximately bell-shaped. Use a 0.030 level of significance to test the claim that the average number of Facebook friends among college students is over 300. Based on the result, should the company start the advertising campaign?

Round to 3 decimal places where appropriate.

(a) State the null and alternative hypotheses, and identify which one is the claim.

H0

:

H1:

Which one is the claim:

• H1

For parts (b), (c) use the correct sign for the t

-value and test statistic.

(b) What is the critical t

-value?

(c) What is the test statistic?

(d) Is the null hypothesis rejected? Is the alternative hypothesis supported?

• Fail to reject H0

and support H1 and fail to support H1 and support H1 and fail to support H1

(e) Select the correct conclusion.

• No, the company should not start the advertising campaign as 300 is less than 306.
• No, the company should not start the advertising campaign as we prove H0
• .

H0

Reject H0

Reject H0

Fail to reject H0

.

At a 0.030 level of significance, the sample data support the claim that the average number of Facebook friends among college students is over 300. The company should start the advertising campaign.

At a 0.030 level of significance, there is not sufficient sample evidence that the average number of Facebook friends among college students is over 300. Based on the research, we cannot conclude that the company should start the advertising campaign.

Yes, the company should start the advertising campaign as 300 is greater than 306.

Yes, the company should start the advertising campaign as we prove H1

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