Question

Please type answer, can't see written answers well.

Also PLEASE PROVIDE BELL SHAPED CURVE** That is the part I struggle with the most.

A Consumer Reports study in February of 2010 found the iPhone customers use an average of 270 megabytes of data per month. Prior to the release of the iPhone 4 during summer of 2010, AT&T was concerned that the average date usage per customer would increase. A random sample of 35 iPhone customers was selected and it found per month was 279 megabytes with a sample standard deviation of 65 megabytes.

a. State the null and alternative hypothesis

b. Using α = .05, is there enough evidence from this sample for AT&T to conclude that the data usage per customer increased following the release of the iPhone 4?

c. Compute the p-value.

d. Repeat the preceding hypothesis test using the critical value approach.

Answer 1

a. State the null and alternative hypothesis

Null hypothesis: H₀: The iPhone customers use an average of 270 megabytes of data per month.

Alternative hypothesis: H_a: The iPhone customers use an average more than 270 megabytes of data per month.

H₀: µ = 270 versus H_a: µ > 270

This is an upper tailed or right tailed test.

b. Using α = .05, is there enough evidence from this sample for AT&T to conclude that the data usage per customer increased following the release of the iPhone 4?

We are given

Level of significance = α = 0.05

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

We are given

Xbar = 279

S = 65

n = 35

df = n – 1 = 35 – 1 = 34

t = (279 – 270) / [65/sqrt(35)]

t = 9/ 10.98700531

t = 0.819149508

Test statistic = t = 0.8191

P-value = 0.2092

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that the data usage per customer increased following the release of the iPhone 4.

There is not enough evidence from this sample for AT&T to conclude that the data usage per customer increased following the release of the iPhone 4.

d. Repeat the preceding hypothesis test using the critical value approach.

We have

Test statistic = t = 0.8191

df = n – 1 = 35 – 1 = 34

α = 0.05

Critical value = 1.6909

(by using t-table)

Test statistic is less than critical value, so we do not reject the null hypothesis.

There is not enough evidence from this sample for AT&T to conclude that the data usage per customer increased following the release of the iPhone 4.