From her firm’s computer telephone log, an executive found that the mean length of 64 telephone calls during July was 4.48 minutes with a standard deviation of 5.87 minutes. She vowed to make an effort to reduce the length of calls. The August phone log showed 48 telephone calls whose mean was 2.396 minutes with a standard deviation of 2.018 minutes. (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value assuming unequal variances. Interpret these results using á = .01. (c) Why might the sample data not follow a normal, bell-shaped curve? If not, how might this affect your conclusions?

c) Isn't this a classic Poisson curve, instead of a Bell curve?

http://en.wikipedia.org/wiki/Poisson_distribution

The data never goes negative, it starts from zero

To answer this question, we can use a two-sample t-test to compare the means of the July and August telephone calls.

(a) The hypotheses for a right-tailed test are as follows:

Null Hypothesis (H0): The mean length of telephone calls in July is equal to or greater than the mean length of telephone calls in August.
Alternative Hypothesis (Ha): The mean length of telephone calls in July is less than the mean length of telephone calls in August.

(b) To obtain a test statistic and p-value, we can follow these steps:

Step 1: Define the significance level (α). In this case, α = 0.01.

Step 2: Calculate the test statistic using the formula:

t = (x1 - x2) / √((s1^2 / n1) + (s2^2 / n2))

where:
x1 = mean length of telephone calls in July
x2 = mean length of telephone calls in August
s1 = standard deviation of telephone calls in July
s2 = standard deviation of telephone calls in August
n1 = number of telephone calls in July
n2 = number of telephone calls in August

Plugging in the values, we have:

t = (4.48 - 2.396) / √((5.87^2 / 64) + (2.018^2 / 48))

Step 3: Calculate the degrees of freedom (df) using the formula:

df = ((s1^2 / n1) + (s2^2 / n2))^2 / (((s1^2 / n1)^2 / (n1 - 1)) + ((s2^2 / n2)^2 / (n2 - 1)))

Plugging in the values, we have:

df = ((5.87^2 / 64) + (2.018^2 / 48))^2 / (((5.87^2 / 64)^2 / (64 - 1)) + ((2.018^2 / 48)^2 / (48 - 1)))

Step 4: Calculate the p-value using the t-distribution with the calculated degrees of freedom. Since we are performing a right-tailed test, we need to find the area to the right of the test statistic.

Step 5: Interpret the results. If the p-value is less than the significance level (α), we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.

(c) The sample data might not follow a normal, bell-shaped curve if the data has outliers, is heavily skewed, or has a small sample size. If the data does not follow a normal distribution, it might affect the accuracy of the t-test results. In such cases, alternative non-parametric tests could be considered.