Question

A local college newsletter reported that the average American college student spends one hour​ (60 minutes) on a social media website daily. But you wonder if there is a difference between males and females. Attached below is a sample of 60 users of the website​ (30 males and 30​ females) and their recorded daily time spent on the website. Complete​ (a) and​ (b) below.

Click the icon to view the sample times.

a. Assuming that the variances in the population of times spent on the website per day are​ equal, is there evidence of a difference in the mean time spent on the website per day between males and​ females? (Use a 0.05 level of​ significance.)

Let

mu 1μ1

be the mean daily time spent on the website for male college students and

mu 2μ2

be the mean daily time spent on the website for female college students. Determine the hypotheses. Choose the correct answer below.

A.

Upper H 0 : mu 1 not equals mu 2H0: μ1≠μ2

Upper H 1 : mu 1 equals mu 2H1: μ1=μ2

B.

Upper H 0 : mu 1 greater than or equals mu 2H0: μ1≥μ2

Upper H 1 : mu 1 less than mu 2H1: μ1<μ2

C.

Upper H 0 : mu 1 less than or equals mu 2H0: μ1≤μ2

Upper H 1 : mu 1 greater than mu 2H1: μ1>μ2

D.

Upper H 0 : mu 1 equals mu 2H0: μ1=μ2

Upper H 1 : mu 1 not equals mu 2H1: μ1≠μ2

Determine the test statistic.

t Subscript STATtSTATequals=nothing

​(Round to two decimal places as​ needed.)

Find the​ p-value.

​p-valueequals=nothing

​(Round to three decimal places as​ needed.)

Daily time spent​ (in minutes) on the website for 30 males
210	960	30	30	10	5	750	270	60	150	150	150	270	270	210
60	90	210	45	150	35	60	60	150	60	15	45	15	120	100

Daily time spent​ (in minutes) on the website for 30 females
60	75	30	60	15	120	120	180	210	15	120	60	60	100	210
60	60	60	270	120	35	60	60	150	60	15	45	15	120	100

Answer 1

Solution:

a) Test of Hypothesis

H0: (i.e, there is no significant difference between mean daily time spent between females and males).

against H1: (i.e, there is a significant difference between mean daily time spent between females and males). (two-tailed)

Option D is correct.

Upper H0 : mu 1 equals mu 2H0: μ1=μ2

Upper H1 : mu 1 not equal mu 2H1: μ1≠μ2

b) Data

Daily time spent​ (in minutes)
females	males
60	210
75	960
30	30
60	30
15	10
120	5
120	750
180	270
210	60
15	150
120	150
60	150
60	270
100	270
210	210
60	60
60	90
60	210
270	45
120	150
35	35
60	60
60	60
150	150
60	60
15	15
45	45
15	15
120	120
100	100

Using Excel

1) Go to "Data". Select "Data Analysis".4

2) Go to "t-Test: Two-Sample Assuming Equal Variances".

3) Select data in input series 1 and 2 boxes. Tick on Label if labels are included in the input data.

4) Click "OK".

Results:

t-Test: Two-Sample Assuming Equal Variances
	Daily time spent​ (in minutes) on the website for 30 females	Daily time spent​ (in minutes) on the website for 30 males
Mean	88.83333333	158
Variance	4066.695402	43338.96552
Observations	30	30
Pooled Variance	23702.83046
Hypothesized Mean Difference	0
df	58
t Stat	-1.739972446
P(T<=t) one-tail	0.043583956
t Critical one-tail	1.671552763
P(T<=t) two-tail	0.087167912
t Critical two-tail	2.001717468

t-statistics= -1.739972446

p-value = 0.087167912

p-vallue also obtained by using TDIST(t-statistics=1.7399,58,2)

Since | t-statistics|= |-1.739972446|< 2.001717468. Hence we do not reject Null Hypothesis. At 5 % level of significance we conclude that , there is no significant difference between mean daily time spent on social media between females and males.