Suppose a paper reported that the freshman year weight gain for the students in a representative sample of 103 freshmen at a midwestern university was 5.8 pounds and that the standard deviation of the weight gain was 6.8 pounds. The authors also reported that 75.7% of these students gained more than 1 pounds, 17.4% maintained their weight within 1 pounds, and 6.8% lost more than 1 pounds.(a)Based on the given information, explain why it is not reasonable to think that the distribution of weight gains for the population of freshmen students at this university is approximately normal.If the distribution of weight gains is approximately normal, for the sample standard deviation ofs = 6.8 poundsand the sample mean ofx = 5.8 pounds,we should see approximately ? 3 5 16 32 % of the weight gain observations be less than one standard deviation below the mean and we should see approximately ? 3 5 16 32 % of the weight gain observations be greater than one standard deviation above the mean. This ---Select--- is is not true, therefore it is not reasonable to think that the distribution of weight gains is approximately normal.(b)Explain why it is reasonable to use a one-sample t confidence interval to estimate the population mean even though the population distribution is not approximately normal. (Select all that apply.)It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at least 30.It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at most 30.It is reasonable to use a one-sample t confidence interval to estimate the population mean since the statistics came from a paper.It is reasonable to use a one-sample t confidence interval to estimate the population mean since all freshman at a midwestern university where surveyed. It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample is representative of the population.(c)Calculate a 95% confidence interval (in pounds) for the population mean weight gain of freshmen students at this university. (Use technology. Round your answers to three decimal places.) , lbsInterpret the interval.We are 95% confident that the weight gain of freshmen students at this university falls within this interval.There is a 95% chance that the true mean number weight gain of freshmen students at this university falls directly in the middle of this interval. There is a 95% chance that the weight gain of freshmen students at this university falls within this interval.We are 95% confident that the true mean weight gain of freshmen students at this university falls within this interval.There is a 95% chance that the weight gain of freshmen students at this university falls directly in the middle of this interval.

Question

Suppose a paper reported that the freshman year weight gain for the students in a representative sample of 103 freshmen at a midwestern university was 5.8 pounds and that the standard deviation of the weight gain was 6.8 pounds. The authors also reported that 75.7% of these students gained more than 1 pounds, 17.4% maintained their weight within 1 pounds, and 6.8% lost more than 1 pounds.(a)Based on the given information, explain why it is not reasonable to think that the distribution of weight gains for the population of freshmen students at this university is approximately normal.If the distribution of weight gains is approximately normal, for the sample standard deviation ofs = 6.8 poundsand the sample mean ofx = 5.8 pounds,we should see approximately  ? 3 5 16 32 % of the weight gain observations be less than one standard deviation below the mean and we should see approximately  ? 3 5 16 32 % of the weight gain observations be greater than one standard deviation above the mean. This  ---Select--- is is not true, therefore it is not reasonable to think that the distribution of weight gains is approximately normal.(b)Explain why it is reasonable to use a one-sample t confidence interval to estimate the population mean even though the population distribution is not approximately normal. (Select all that apply.)It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at least 30.It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at most 30.It is reasonable to use a one-sample t confidence interval to estimate the population mean since the statistics came from a paper.It is reasonable to use a one-sample t confidence interval to estimate the population mean since all freshman at a midwestern university where surveyed. It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample is representative of the population.(c)Calculate a 95% confidence interval (in pounds) for the population mean weight gain of freshmen students at this university. (Use technology. Round your answers to three decimal places.) ,  lbsInterpret the interval.We are 95% confident that the weight gain of freshmen students at this university falls within this interval.There is a 95% chance that the true mean number weight gain of freshmen students at this university falls directly in the middle of this interval.     There is a 95% chance that the weight gain of freshmen students at this university falls within this interval.We are 95% confident that the true mean weight gain of freshmen students at this university falls within this interval.There is a 95% chance that the weight gain of freshmen students at this university falls directly in the middle of this interval.

Accepted Answer

(a). Explain the reason for the distribution of weight gains for the population of freshmen students…