14722 a) 3. According to CTIA- The wireless Association, the mean monthly cell p
ID: 3321852 • Letter: 1
Question
14722 a) 3. According to CTIA- The wireless Association, the mean monthly cell phone bll n 2014 was $ 85.27.A market researcher believes that the mean monthly cell phone bill is different today, but is not sure whether bills have declined because of technological advances or increased due to additional use.The researcher phones a simple random sample of 12 cell phone subscribers and finds that their mean monthly bill is $ 87.05. The population standard deviation is $18.49. Use 0.05 level of significance to determine whether the mean monthly cell phone billsis different today from $ 85.27 a) Set up the null and alternative hypotheses for the test. b) Compute the test statistic. c) What's the p-value for this test d) What decision can be made at the 0.05 level of significance e) Give the appropriate conclusion for the test.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 85.27
Alternative hypothesis: 85.27
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 5.338
DF = n - 1 = 12 - 1
D.F = 11
t = (x - ) / SE
t = 0.33
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the t statistic having 11 degrees of freedom is less than - 0.333 or greater than 0.333.
Thus, the P-value = 0.7414
Interpret results. Since the P-value (0.7414) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that mean phone bill is different from $85.27.
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