Question

A 2018 Pew Research poll found that 78% of smart phone owners use their phone for online shopping. You take a random sample now of 150 current smart phone owners and find that 133 of them use their phone for shopping. Is this evidence that since 2018 there has been an increase in the proportion of smart phone owners who use their devices for shopping? Justify your conclusion at  a= 0.01. (a) What test should you conduct here? (b) State the hypotheses and the test statistic (c) Find the p-value. (d) What conclusion do you reach based on your p-value? Summarize in context.

Answer 1

Result:

A 2018 Pew Research poll found that 78% of smart phone owners use their phone for online shopping. You take a random sample now of 150 current smart phone owners and find that 133 of them use their phone for shopping. Is this evidence that since 2018 there has been an increase in the proportion of smart phone owners who use their devices for shopping? Justify your conclusion at a a= 0.01.

(a) What test should you conduct here?

Single sample proportion test ( z test) is used here.

(b) State the hypotheses and the test statistic

Ho: P=0.78, H1: P > 0.78

Z test is used

(c) Find the p-value.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.78
Level of Significance	0.01
Number of Items of Interest	133
Sample Size	150
Intermediate Calculations
Sample Proportion	0.886666667
Standard Error	0.0338
Z Test Statistic	3.1537
Upper-Tail Test
Upper Critical Value	2.3263
p-Value	0.0008
Reject the null hypothesis

Z test statistic = 3.1537

P value: 0.0008

(d) What conclusion do you reach based on your p-value? Summarize in context.

Since p value < 0.01 level of significance, Ho is rejected.

We conclude that there is sufficient evidence that since 2018 there has been an increase in the proportion of smart phone owners who use their devices for shopping.