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Answer :
Final answer:
To construct a 98% confidence interval for the mean number of hours a student studies per week, use the formula: Confidence Interval = sample mean ± z * (population standard deviation / √sample size).
Explanation:
To construct a 98% confidence interval for the mean number of hours a student studies per week, we can use the formula: Confidence Interval = sample mean ± z * (population standard deviation / √sample size).
In this case, the sample mean is 20, the population standard deviation is 2, and the sample size is 56. The z-value for a 98% confidence level is 2.33. Plugging these values into the formula:
Confidence Interval = 20 ± (2.33 * (2 / √56))
Calculating the expression, we get:
Confidence Interval ≈ 20 ± 0.626
Rounding to two decimal places, the confidence interval is approximately (19.37, 20.63).
Therefore, we can say with 98% confidence that the mean number of hours a student studies per week falls between 19.37 and 20.63 hours.
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