Question

According to a​ report, the mean of monthly cell phone bills was ​$49.85 three years ago. A researcher suspects that the mean of monthly cell phone bills is less today. ​(a) Determine the null and alternative hypotheses. ​(b) Explain what it would mean to make a Type I error. ​(c) Explain what it would mean to make a Type II error. ​(a) State the hypotheses. Upper H 0​: mu equals ​$ 49.85 49.85 Upper H 1​: mu greater than ​$ 49.85 49.85 ​(Type integers or decimals. Do not​ round.) ​(b) Explain what it would mean to make a Type I error. Choose the correct answer below. A. The sample evidence did not lead the researcher to believe the mean of the monthly cell phone bill is different from ​$49.85​, when in fact the mean of the bill is different from ​$49.85. B. The sample evidence did not lead the researcher to believe the mean of the monthly cell phone bill is less than ​$49.85​, when in fact the mean of the bill is less than ​$49.85. C. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is different from ​$49.85​, when in fact the mean of the bill is $ 49.85 . D. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is less than ​$49.85​, when in fact the mean of the bill is ​$49.85. ​(c) Explain what it would mean to make a Type II error. Choose the correct answer below. A. The sample evidence did not lead the researcher to believe the mean of the monthly cell phone bill is different from ​$49.85​, when in fact the mean of the bill is different from ​$49.85. B. The sample evidence did not lead the researcher to believe the mean of the monthly cell phone bill is less than ​$49.85​, when in fact the mean of the bill is less than ​$49.85. C. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is less than ​$49.85​, when in fact the mean of the bill is ​$49.85. D. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is less than ​$49.85​, when in fact the mean of the bill is less than ​$49.85.

Answer 1

(A) given that we have to test whether the mean is less than 49.85 or not. So, it is a left tailed hypothesis test

so, we can write hypotheses as

(B) We know that type I error is the rejection of a true null hypothesis

In this case type I error would be that "rejecting the hypothesis that the mean is equal to 49.85 and concluding that it is less than 49.85, when in fact, the mean was equal to 49.85"

so, option D is correct

(C) We know that type II error is the failure to reject a false null hypothesis

In this case type II error would be that "rejecting the hypothesis that the mean is less than 49.85 and concluding that it is equal to 49.85, when in fact, the mean was less than 49.85"

so, option B is correct