Final answer:
The null hypothesis for this test is that the mean time spent checking work email for white-collar workers in the United States is equal to half of the 8-hour work day, which is 4 hours. The alternative hypothesis is that the mean time spent checking work email is greater than 4 hours.
Step-by-step explanation:
The null hypothesis for this test is that the mean time spent checking work email for white-collar workers in the United States is equal to half of the 8-hour work day, which is 4 hours. The alternative hypothesis is that the mean time spent checking work email is greater than 4 hours.
The test statistic for this hypothesis test is calculated using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
The p-value is then calculated using the t-distribution with the degrees of freedom equal to the sample size minus 1. The p-value represents the probability of observing a test statistic as extreme as the one calculated or more extreme, assuming the null hypothesis is true.
In this case, the test statistic is calculated to be approximately 1.666. Looking up this value in the t-distribution table with 25 degrees of freedom (sample size minus 1), the corresponding p-value is approximately 0.056.
Since the p-value is greater than the significance level of 0.05, we do not have enough evidence to reject the null hypothesis. Therefore, at a significance level of 0.05, the correct conclusion is option c: There is not enough evidence to conclude that the mean number of hours is more than 4.5.