Question

Market researchers wondered if teens were more or less likely than adults to use their mobile phone as an alarm clock. The researchers surveyed a random sample of people and removed those who didn't have a mobile phone. Here are the results:The researchers want to test if these results suggest a significant difference between the proportions of teens and adults that use their phone as an alarm clock. Assume that all conditions have been met.Which of the following would be an appropriate test statistic for their test?

Answer 1

The appropriate test statistic to use is the two-sample z-test for comparing proportions. This test compares the difference between two sample proportions and determines if it is statistically significant.

Step-by-step explanation:

To test if the results suggest a significant difference between the proportions of teens and adults that use their phone as an alarm clock, the appropriate test statistic to use is the two-sample z-test for comparing proportions. This test compares the difference between two sample proportions and determines if it is statistically significant.

Formulate the hypotheses: The null hypothesis (H0) is that there is no difference between the proportions of teens and adults using their phone as an alarm clock. The alternative hypothesis (H1) is that there is a significant difference between the proportions.

Calculate the test statistic: Calculate the z-test statistic using the formula for comparing proportions: z = (p1 - p2) / sqrt((p ×(1 - p)) / n1 + (p ×(1 - p)) / n2), where p1 and p2 are the sample proportions, p is the pooled proportion, and n1 and n2 are the sample sizes.

Find the p-value: Determine the p-value associated with the test statistic using a standard normal distribution table or a statistical software.

Make a decision: Compare the p-value to the significance level (usually 0.05) to determine if there is enough evidence to reject the null hypothesis.

Answer 2

To test for a significant difference between the proportions of teens and adults using their phone as an alarm clock, the appropriate test statistic would be the z-test for comparing two proportions.

Step-by-step explanation:

To test if there is a significant difference between the proportions of teens and adults that use their phone as an alarm clock, the appropriate test statistic to use is the z-test for comparing two proportions.

The formula for the test statistic is:

z = (p1 - p2) / √(p * (1-p) * ((1/n1)+(1/n2)))

where:

• p1 and p2 are the sample proportions of teens and adults using their phone as an alarm clock
• p is the overall proportion of both teens and adults using their phone as an alarm clock
• n1 and n2 are the sample sizes for teens and adults