Final answer:
To calculate the 99% confidence interval for the average browsing time, the t-distribution is used due to the sample size of 31. The confidence interval is constructed by adding and subtracting the margin of error from the sample mean. The correct confidence interval is 62.0886 < μ < 63.9114.Therefore, the correct option is:c) 62.2314<μ<63.7686
Step-by-step explanation:
To construct a 99% confidence interval for the mean number of minutes the office workers spend browsing the web, we first define the necessary components:
Sample mean (x): 63 minutes
Standard deviation (s): 2.1 minutes
Sample size (n): 31 workers
Because the sample size is less than 30, we use the t-distribution to calculate the confidence interval. Since we do not know the degrees of freedom for the confidence interval, we will use the closest available value from the t-distribution table or software, which is often 30 for 31 samples. However, for accuracy, you would normally subtract 1 from the sample size to find the correct degrees of freedom, resulting in 30 degrees of freedom in this case.
To find the margin of error (E), we use the t-distribution critical value (tα/2) corresponding to the 99% confidence level and 30 degrees of freedom. The margin of error E is computed as:
E = tα/2 × (s/√n)
Next, we calculate the confidence interval:
Confidence interval = x ± E
Choosing the correct tα/2 value and computing E, we then establish the confidence interval limits by adding and subtracting E from the sample mean. Finally, we round the results to four decimal places to form the 99% confidence interval for the mean number of minutes spent browsing the web.
The correct confidence interval from the choices provided would be option (a) 62.0886 < μ < 63.9114. This represents that we are 99% confident that the true mean number of browsing minutes falls between 62.0886 and 63.9114 minutes.Therefore, the correct option is:c) 62.2314<μ<63.7686