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 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 obtains the monthly bills
94.25 38.94 79.15 56.78
70.07 115.59 77.56 37.01
55.00 76.05 27.29 52.48
Assuming SD=$18.49 and normal curve shape for the 2004 distribution of bills price, use the sample data to
determine whether the mean monthly cell phone bills is different from $50.64 at the p=0.05 level of
significance.
To determine whether the mean monthly cell phone bills are different from $50.64 at the p=0.05 level of significance, we can conduct a t-test.
The null hypothesis (H0) is that there is no significant difference between the mean monthly cell phone bills and $50.64. The alternative hypothesis (Ha) is that there is a significant difference.
We can calculate the test statistic using the formula:
t = (x̄ - μ) / (σ / √n),
where:
x̄ is the sample mean = (94.25 + 38.94 + 79.15 + 56.78 + 70.07 + 115.59 + 77.56 + 37.01 + 55.00 + 76.05 + 27.29 + 52.48) / 12 = 64.8725,
μ is the population mean = $50.64,
σ is the population standard deviation = $18.49,
n is the sample size = 12.
Plugging the values into the formula, we get:
t = (64.8725 - 50.64) / (18.49 / √12).
Next, we need to calculate the degrees of freedom (df) which is equal to n - 1.
df = 12 - 1 = 11.
Using the t-distribution table or a statistical software, we can find the critical t-value at the p=0.05 level of significance for a two-tailed test with 11 degrees of freedom. Let's assume the critical t-value is 2.201.
Now, we can compare the calculated t-value to the critical t-value. If the calculated t-value is greater than the critical t-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Calculate t:
t = (64.8725 - 50.64) / (18.49 / √12) ≈ 2.192.
Since the calculated t-value (2.192) is less than the critical t-value (2.201), we fail to reject the null hypothesis.
Therefore, based on the sample data, there is not enough evidence to conclude that the mean monthly cell phone bills are different from $50.64 at the p=0.05 level of significance.