Question

according to a 2015 survey by mobile loyalty company sessionm, 47% of smartphone users preferred online shopping to in - store shopping. a professor at a local community college believes that the percentage of smartphone users who prefer online shopping may be higher among community college students.
she randomly selects 150 community college students with smartphones and she finds that 84 of the students surveyed prefer online shopping. in testing the hypotheses: ( h_0:p = 0.47 ) versus ( h_a:p>0.47 ), she calculates the test statistic as ( z = 2.21 ). the alpha level for this problem is 0.05. use the normal table to identify the appropriate p - value for this z score.
click here to access the normal table.
given these results, which of the following is an appropriate conclusion?
a. there is enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p - value = 0.0136).
b. there is enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p - value = 0.0172).
c. there is not enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p - value = 0.9864).
d. there is not enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p - value = 0.0136).

Explanation:

Step1: Find the p - value

For a one - tailed test (since \(H_{a}:p>0.47\)), the p - value is \(P(Z > 2.21)\).
We know that \(P(Z\leq z)\) can be found from the standard normal table. For \(z = 2.21\), \(P(Z\leq2.21)=0.9864\).
Then \(P(Z > 2.21)=1 - P(Z\leq2.21)\).

Step2: Calculate the p - value

Substitute the value from the table: \(P(Z > 2.21)=1 - 0.9864=0.0136\).

Step3: Make a decision

Since the p - value (\(0.0136\)) is less than the significance level \(\alpha = 0.05\), we reject the null hypothesis \(H_{0}:p = 0.47\).

So, there is enough evidence to support the claim that more than 47% of community college students with smartphones prefer online shopping.

Answer:

A. There is enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p - value = 0.0136).