Question

An online survey asked 1,000 adults “What do you buy from your mobile device?” The results indicated that 61% of the females and 39% of the males answered clothes.

The sample sizes for males and females were not provided. Suppose that both samples were 500 and that 195 out of the 500 males and 305 out of the 500 females reported they buy clothing from their mobile device.

Using the Excel output below, answer the following questions:

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.01
Group 1
Number of Items of Interest	195
Sample Size	500
Group 2
Number of Items of Interest	305
Sample Size	500
Intermediate Calculations
Group 1 Proportion	0.39
Group 2 Proportion	0.61
Difference in Two Proportions	-0.22
Average Proportion	0.5000
Z Test Statistic	-6.9570
Two-Tail Test
Lower Critical Value	-2.5758
Upper Critical Value	2.5758
p-Value	0.0000
Reject the null hypothesis

a) Is there evidence of the difference between males and females in the proportion who said they buy clothing from their mobile device at the 0.01 level of significance?

b) What is the null hypothesis?

c) What is the correct t-statistic?

d) What is the correct decision rule?

e) What is the correct conclusion?

f) Using only the p-value, what is the conclusion?

Answer 1

a) There is enough evidence to conclude that there is significance difference between males and females in the proportion who said they buy clothing from their mobile deviceat the 0.01 level of significance.

b) Null Hypothesis:

H_{​​​​​​0} : There is no Significance difference between males and females in the proportion who said they buy clothing from their mobile device.

i.e. H_{​​​​​0} : P_{​​​​​​1}=P_{​​​​​​2}

Alternative Hypothesis:

H_{​​​​​1} : There is Significance difference between males and females in the proportion who said they buy clothing from their mobile device.

i.e. H_{​​​​1} : P_{​​​​​​1} P_{​​​​​​2}

P_{​​​​​​1} = population proportion of males who said they buy clothing from their mobile device

P_{​​​​​2} = population proportion of females who said they buy clothing from their mobile device

p_{​​​​​​1} = sample proportion of males who said they buy clothing from their mobile device= X_{​​​​​​1}/ n_{​​​​​​1}​​​=0.39

p_{​​​​​2} = sample proportion of females who said they buy clothing from their mobile device=X_{​​​​​2}/ n_{​​​​​2}= 0.61

X_{​​​​​​1} = number of males who said they buy clothing from their mobile device=195

X_{​​​​​2} = number of females who said they buy clothing from their mobile device=305

n_{​​​​​1} =sample size of males=500

n_{​​​​​1} =sample size of females=500

c)Test statistic:

To test the above Hypothesis the equality of two population proportion z -test static is: hence n > 30

Z= -6.9570

Cal | Z| = 6.9570

= 0.5

= 0.5

d) critical value for two tailed Hypothesis is = 2.5758at % level of Significance

If Cal |Z| >  

Then we reject H_{​​​​0} at % level of Significance.

f) p- value for the test statistic and 1% level of Significance is :

p- value = 0.0000

e) The p- value < 0.01

From the p-value and critical value we reject the null hypothesis.

Conclusion:

There is enough evidence to conclude that there is Significance difference between males and females in the proportion who said they buy clothing from their mobile device.