According to a Pew Research Center, in May 2011, 35% of all American adults had a smartphone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.She selects 300 community college students at random and finds that 120 of them have a smartphone. In testing the hypotheses H0, P = 0.35, versus Ha, p > 0.35, she calculates the test statistic as Z = 1.82.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? There is enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.034). There is enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.068). There is not enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.966). There is not enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.034).
Question
According to a Pew Research Center, in May 2011, 35% of all American adults had a smartphone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.She selects 300 community college students at random and finds that 120 of them have a smartphone. In testing the hypotheses H0, P = 0.35, versus Ha, p > 0.35, she calculates the test statistic as Z = 1.82.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? There is enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.034). There is enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.068). There is not enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.966). There is not enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.034).
Solution
The Z score of 1.82 corresponds to a p-value of approximately 0.034 (you can confirm this using a Z-table or an online calculator). This p-value is less than the commonly used significance level of 0.05, which suggests that the observed data is unlikely under the null hypothesis (H0: P = 0.35).
Therefore, the professor has enough evidence to reject the null hypothesis in favor of the alternative hypothesis (Ha: p > 0.35). This means that there is enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.034).
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