Question

Many families have decided to use their TVs for broadband-delivered video (for example, from Netflix, Hulu and Sling) instead of pay-TV (cable and satellite) services. A local cable TV provider in Kansas City, Missouri, Spectrum Cable, is concerned about losing market share and plans to conduct a hypothesis test to determine whether more advertising is needed. A random sample of homes in the city will be obtained, and the data will be used to determine whether there is any evidence that the true proportion of homes with broadband-delivered video is greater than 0.30.

Describe type I and type II errors in this context.
A. A type I error would be to conclude the population proportion of homes with broadband-delivered video is more than 0.30 when it is actually 0.30 or less. A type II error would be continuing to believe the population proportion of homes with broadband-delivered video is, at most, 0.30 when it is actually more than 0.30.

B. A type I error would be continuing to believe the population proportion of homes with broadband-delivered video is, at most, 0.30 when it is actually more than 0.30. A type II error would be to conclude the population proportion of homes with broadband-delivered video is more than 0.30 when it is actually 0.30 or less.

C. A type I error would be to conclude the population proportion of homes with broadband-delivered video is more than 0.30 when it is more than 0.30. A type II error would be continuing to believe the population proportion of homes with broadband-delivered video is, at most, 0.30 when it actually is, at most, 0.30.

D. A type I error would be to conclude the population proportion of homes with broadband-delivered video is less than 0.30 when it is actually 0.30 or more. A type II error would be continuing to believe the population proportion of homes with broadband-delivered video is, 0.30 when it is actually less than 0.30.

Answer 1

The Type I error is falsely rejecting the null hypothesis, while the Type II error is failing to reject the false null hypothesis.

Step-by-step explanation:

The Type I error in this context would be to conclude that the proportion of homes with broadband-delivered video is more than 0.30 when it is actually 0.30 or less. The Type I error is falsely rejecting the null hypothesis, while the Type II error is failing to reject the false null hypothesis.

This means falsely rejecting the null hypothesis. On the other hand, the Type II error would be to continue to believe that the proportion of homes with broadband-delivered video is at most 0.30 when it is actually more than 0.30, which means failing to reject the null hypothesis when it is false.