A researcher is interested in finding a 98% confidence interval for the mean number of minutes students are concentrating on their professor during a one-hour statistics lecture. The study included 135 students who averaged 32.4 minutes concentrating on their professor during the hour lecture. The standard deviation was 11.4 minutes. Round answers to three decimal places where possible.a. To compute the confidence interval use a [ ? ] distribution.b. With 98% confidence the population mean minutes of concentration is between [ ____ ] and [ ____ ] minutes.c. If many groups of 135 randomly selected members are studied, then a different confidence interval would be produced from each group. About [ ____ ] percent of these confidence intervals will contain the true population mean minutes of concentration and about [ ____ ] percent will not contain the true population mean minutes of concentration.

Given that:To find:a. The distribution to be used to find the confidence interval.b. 98% confidence interval for the mean number of times students are concentrating on their professor during a one hour statistics lecture.c. Interpretation of the obtained 98% confidence interval.Since the population standard deviation is unknown here, we have to use t-distribution in order to compute the required confidence interval.In statistics, a sample size of 135 is not considered small. The t-distribution is typically used when the sample size is less than 30. However, it’s also used when the population standard deviation is unknown, which is the case here. So even with a sample size of 135, using the t-distribution would be appropriate because we don’t know the population standard deviation.Using the given information, the level of significance can be calculated asAnd the degrees of freedom for the critical t value will be:Thus, the critical t value will be:This critical t value is calculated using Excel as follows:Now, the margin of error can be calculated as:Now, after knowing the margin of error, the required 98% confidence can be computed as:Hence, the required 98% confidence interval for the mean number of times students are concentrating on their professor during a one hour statistics lecture is (30.090, 34.710).The confidence interval that we have calculated, (30.090, 34.710) means that we can be 98% confident that the true population mean of the number of minutes students are concentrating on their professor during a one hour statistics lecture is between 30.090 and 34.710 minutes.In other words, if we were to take many samples and calculate the confidence interval for each sample, about 98% of these intervals would contain the true population mean.a. To compute the confidence interval use a t distribution.b. With 98% confidence the population mean minutes of concentration is between 30.090 and 34.710 minutes.c. If many groups of 135 randomly selected members are studied, then a different confidence interval would be produced from each group. About 98 percent of these confidence intervals will contain the true population mean minutes of concentration and about 2 percent will not contain the true population mean minutes of concentration.