According to a survey, 24% of households relied solely on their cell phones for

Question

According to a survey, 24% of households relied solely on their cell phones for phone service instead of landlines. It was also reported that this percentage has steadily increased over the previous years. A phone company would like to sample 145 households randomly to test the hypothesis that the proportion of cell phone-only households increased. Complete parts a through d below. a. Explain how Type I and Type II errors can occur in this hypothesis test A Type I error can occur when the researcher concludes the average percentage of households relying on a cell phone but the percentage A Type II error can occur when the researcher concludes that the percentage of households relying on a cell phone when, in fact, the percentage of households relying on a cell phone b. Using alpha=0.10, calculate the probability of a Type II error occurring if the actual proportion of cell phone-only households is 0.33. The probability of a Type II error occurring is . (Round to four decimal places as needed.) C. Using alpha= 0.05, calculate the probability of a Type II error occurring if the actual proportion of cell phone-only households is 0.33. The probability of a Type II error occurring is . (Round to four decimal places as needed.) d. Explain the differences in the results calculated in parts b and c. A. When alpha is decreased, the probability of committing a Type II error decreases. B. When alpha is increased, the probability of committing a Type II error increases. C. When alpha is decreased, the probability of committing a Type II error stays constant D. When alpha is increased, the probability of committing a Type II error decreases.

Explanation / Answer

a) Type I error is is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is the failure to reject a false null hypothesis (a "false negative")

Hence here it is concluding that average percent of households relying on the cell phone increased but percentage was only 24%

Type II error is to conclude that average percent of households relying on the cell phone is 24% while the percen >24%

b) When alpha = 0.10, Type II error =0.0000

c) 0.0000

d) Option C is right

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