For a sample of 50 days, George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?
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To determine if there is a significant difference in the mean number of calls per day between two employees (George Murnen and another employee), we can use a t-test. The given information states that George Murnen made an average of 5.02 calls per day for a sample of 50 days.
To perform the t-test, we need to know the mean and standard deviation of the sample data for the other employee. Unfortunately, this information is not provided, so we cannot calculate the t-test directly. However, we can calculate the p-value given the information provided.
The null hypothesis (H0) in this case is that there is no difference in the mean number of calls per day between the two employees. The alternative hypothesis (H1) is that there is a difference.
To calculate the p-value, we can use a t-distribution table or statistical software. Since the sample size is large enough (n = 50), we can assume that the sampling distribution is approximately normally distributed.
The test statistic for a two-sample t-test is given by the formula:
t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))
Where:
x1 and x2 are the sample means
s1 and s2 are the sample standard deviations
n1 and n2 are the sample sizes
Since we do not have the sample data for the other employee, we cannot calculate the test statistic directly. However, we can calculate the p-value using the given information.
The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. In this case, it is the probability of observing a difference in the mean number of calls per day as extreme as 5.02, or more extreme, assuming no difference between the two employees.
To calculate the p-value, we can use statistical software or an online calculator. Using the information provided, the p-value can be determined to assess if there is a significant difference in the means of the two employees.