Question

In: Statistics and Probability

10. According to a 2018 report, the mean amount of data used by all smartphone users...

10. According to a 2018 report, the mean amount of data used by all smartphone users with unlimited data plans was 4.87 GB per month. A company would like to determine if the mean amount of data used per month by smartphone user is different that it was in 2018. In order to investigate the issue, random sample of 900 smartphone users was selected.

Determine the null and alternative hypotheses:

H0=

HA=

A Type I error in the context of this problem would be:

A Type II error in the context of this problem would be:

11. According to a report published last year by Pew Research, 23% of all American adults lived in a middle-class household. This year, an economist collected data from a random sample of 1210 American adults in order to determine if the percent of American adults who live in a middle-class household is lower than 23%. State the hypotheses and explain the possible Type 1 and Type 2 errors.

Determine the null and alternative hypotheses:

H0=

HA=

A Type I error in the context of this problem would be:

A Type II error in the context of this problem would be:

Solutions

Expert Solution

Null hypothesis: the mean amount of data used by all smartphone users with unlimited data plans is 4.87 GB

H0=

Alternate hypothesis: the mean amount of data used by all smartphone users with unlimited data plans is not equal to 4.87 GB

HA=

Type I error in the context of this problem would be:

P[ rejecting H0 when it is true ] = The research claims that the mean is different from 4.87 but in reality it is 4.87

Type II error in the context of this problem would be:

c= The research claims that the mean is 4.87 but in reality it is not.

Null hypothesis: Proportion of American adults lived in a middle-class household is 23%

H0= p = 0.23

Alternate hypothesis: Proportion of American adults lived in a middle-class household is less than 23%

HA= p < 0.23

Type I error in the context of this problem would be:

P[ rejecting H0 when it is true ] = Research claims that the proportion is less than 0.23 but in reality it is 0.23

Type II error in the context of this problem would be:

P[ rejecting H0 when it is true ] = Research claims that the proportion is 0.23 but in reality it is less than 0.23

orchestra answered 11 months ago

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