According to CTIA-The Wireless Association, the mean monthly cell phone bill in

Question

According to CTIA-The Wireless Association, the mean monthly cell phone bill in 2004 was $50.64. A market researcher believes that the mean monthly cell phone bill is different t but is not sure whether bills have declined because of technological advances or increase to additional use. To test the claim, the researcher phones a simple random sample of phone subscribers and obtains a sample mean of 65.014. Assuming the population standard deviation is $18.49, use the data to test the claim that the mean monthly cell phone bill is different at the : .05 level of significance. Identify the null and alternative hypothesis. Show the confidence interval needed to test the null hypothesis. State if the null hypothesis should be accepted or rejected. 15 oday. d due 12 cell

Explanation / Answer

Let X = monthly cell phone bill.

Then, we assume X ~ N(µ, 2), where µ is unknown but hypothesized to be 50.64 and 2 is given to be 18.49.

Claim:

Mean monthly cell phone bill is different from 50.64

Hypotheses:

Null H0: µ = µ0 = 50.64   Vs Alternative HA: µ 50.64

The corresponding Confidence Interval for the population mean to test this hypothesis at level of significance % is: 100(1 - ) % CI given by:

{Xbar ± (/n)(Z/2)} = 65.014 ± (18.49)/(12)(Z0.025) [given = 0.05]

= 65.014 ± 10.462

= (54.552, 75.476)

Decision

Since the 95% CI does not contain 50.64, Null H0: µ = 50.64 is rejected.

=> the claim is valid

DONE

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