Question

6. In 2013 the average number of times individuals under 30 years old accessed Facebook on a daily basis was 14.9. An ad agency promoting the necessity of marketing on social media believes this number is now higher. In an effort to prove its claim, it randomly samples 28 individuals under 30 years old and determines their daily access to Facebook. The measurements appear below. Assuming the underlying distribution is normal, is there sufficient evidence at the 0.10 level to substantiate the ad agency's claim?

12 8 16 15 22 11 12 9 21 15 14 18 17 27 16 33 13 16 15 12 19 10 21 11 11 17 20 24

a. Give the null and alternative hypotheses for this test.

H0:

H1:

b. Determine the value of the test statistic.

c. Determine the appropriate critical value(s).

d Determine the P-value.

e. Is there sufficient evidence to support the claim that the mean number of times individuals under 30 years old daily access Facebook is greater than 14.9? Explain your reasoning.

Answer 1

a. Here claim is that mean is now higher

So vs

b. For the given sample mean is

Create the following table.

data	data-mean	(data - mean)2
12	-4.25	18.0625
8	-8.25	68.0625
16	-0.25	0.0625
15	-1.25	1.5625
22	5.75	33.0625
11	-5.25	27.5625
12	-4.25	18.0625
9	-7.25	52.5625
21	4.75	22.5625
15	-1.25	1.5625
14	-2.25	5.0625
18	1.75	3.0625
17	0.75	0.5625
27	10.75	115.5625
16	-0.25	0.0625
33	16.75	280.5625
13	-3.25	10.5625
16	-0.25	0.0625
15	-1.25	1.5625
12	-4.25	18.0625
19	2.75	7.5625
10	-6.25	39.0625
21	4.75	22.5625
11	-5.25	27.5625
11	-5.25	27.5625
17	0.75	0.5625
20	3.75	14.0625
24	7.75	60.0625

So

So test statistics is

c. The t-critical value for a right-tailed test, for a significance level of α=0.10 is

tc​=1.314

Graphically

d.Here P value is TDIST(1.25,27,1)=0.1110

e. As P value is greater than alpha=0.10 and t statistics is not in the rejection region, we fail to reject the null hypothesis

Is there no sufficient evidence to support the claim that the mean number of times individuals under 30 years old daily access Facebook is greater than 14.9