Question

A social psychologist claims to know how many casual friends are in the typical person's social network.  The psychologist states that the average number of casual friends is 11.  You question the validity of this researcher's claim and decide to conduct your own study.  You interview a random sample of people and determine for each the number of friends or social acquaintances they see or talk to at least once a year.  Your data are below:

16	4	6	11	16	4
8	7	8	3	10	6
9	21	14	12	9	11

Test if your results differ from the social psychologist's claim, with an alpha of .05.

a. State the H₀ and H₁ hypotheses, in statistical notation, and identify the critical t value(s).

b. Calculate standard error and the observed t-statistic.  What is your decision regarding the null hypothesis?  Why?

c. State your results in nonstatistical terms.

Answer 1

the necessary calculation table:-

x	x2
16	256
8	64
9	81
4	16
7	49
21	441
6	36
8	64
14	196
11	121
3	9
12	144
16	256
10	100
9	81
4	16
6	36
11	121
sum=175	sum=2087

sample size (n) = 18

a).hypothesis:-

df = (n-1)= (18-1) = 17

the critical value of t be:-

[ from t distrbution table for df =17,alpha=0.05,both tailed test]

b).standard error be:-

test statistic be:-

decision:-

so, we fail to reject the null hypothesis.

c).there is sufficient evidence to support the social psychologist's claim at 0.05 level of significance.my results do not differ from the social psychologist's claim.

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