Question

According to the financial reports by​ Snapchat, the average daily user of Snapchat created 19 ​messages, or​ "snaps," per day in Q3 2017. A college student wants to find out if the number of Snapchat messages has changed since Q3 2017 and creates a random sample using information from students on her campus for the current​ semester, with the accompanying results. Complete parts a through

c. Click the icon to view the daily snaps data.

22 14 20 33 13

9 17 30    6 21

17 31 10 23 26

27 22 33 19 16

a. Using alpha α=0.05​, test the hypothesis that the number of Snapchats sent by the average Snapchat user has not changed since Q3 2017.

Determine the null and alternative hypotheses.

H0​: μ not equals ≠ greater than or equals ≥ equals = less than or equals ≤

H1​: μ ▼ not equals ≠ less than < equals = greater than > ​(Type integers or decimals. Do not​ round.)

Determine the appropriate critical value. Select the correct choice below and fill in the answer box within your choice. ​(Round to three decimal places as​ needed.)

A. - tα equals =

B. tα=

C.tα/2=

Calculate the appropriate test statistic. t=

t-x= ​(Round to two decimal places as​ needed.)

State the conclusion.

(Reject/Do not reject) H0. There ▼(is/is not) sufficient evidence to conclude that the number of Snapchats sent by the average Snapchat user has (increased/changed/not changed/decreased) since Q3 2017.

b. Determine the precise​ p-value for this test using Excel.

The​ p-value is . ​(Round to three decimal places as​ needed.

c. What assumptions need to be made to perform this​ analysis? Select all that apply.

A. The sample is large.

B. The population is normally distributed.

C. No assumptions are necessary.

D. The population standard deviation is small.

E. The sample mean is large.

Answer 1

	X	X^2
1	22	484
2	14	196
3	20	400
4	33	1089
5	13	169
6	9	81
7	17	289
8	30	900
9	6	36
10	21	441
11	17	289
12	31	961
13	10	100
14	23	529
15	26	676
16	27	729
17	22	484
18	33	1089
19	19	361
20	16	256
Total	409	9559
Mean	20.45
SD	7.930

Mean =

SD =

a. Using alpha α=0.05​, test the hypothesis that the number of Snapchats sent by the average Snapchat user has not changed since Q3 2017.

In 2017 the sc created were 19 per day. so this our null mean. Since we are checking for the difference a change it is two tailed hypothesis.

Determine the appropriate critical value. Select the correct choice below and fill in the answer box within your choice. ​(Round to three decimal places as​ needed.)

Here we do not have the population SD and we are checking for the population mean so we will use a t-dist for this test. We assume that the sample comes from a normal population.

C.

= 2.0930   ...................using t-dist tables df = 19 p =0.025

Calculate the appropriate test statistic.

Test stat =

Test stat = 0.8177

State the conclusion.

Since |test stat | < Critical value

Do not reject  H0. There is not sufficient evidence to conclude that the number of Snapchats sent by the average Snapchat user has changed since Q3 2017.

b. Determine the precise​ p-value for this test using Excel.

The​ p-value = 2 P( > |Test Stat | )

= 2 * P( > 2.09)

= 2 * 0.2118 ...........using t-dist tables with f = 19 and x = 2.09

p-value = 0.4237

c. What assumptions need to be made to perform this​ analysis? Select all that apply.

A. The sample is large.

since we assume that means of these large sample are normally distributed.

B. The population is normally distributed.

One of these has to be made

C. No assumptions are necessary.

D. The population standard deviation is small.

E. The sample mean is large.