Question
Please answer parts D-H ! According to a Gallup poll conducted in October 2017, Americans planned to spend $907 orn Christmas gifts, an increase of $121 over the previous year. Results for this Gallup poll were based on telephone interviews conducted Oct. 5-11,2017, with a random sample of 1,028 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia. A. Is $907 a parameter or a statistic? Explain. (1 pt) B. For this study identify the population of interest, sample selected and parameter of interest. (1 pt) Let denote the true mean amount that was expected to be spent on Christmas gifts among those in the population and let represent the standard deviation of these amounts. C. Is it possible that the sample mean was $907 even if turned out to be $899? what if was equal to $885? What about $1000? (1 pt) D. Assume that -$250, what does the Central Limit Theorem say about how the sample mean would vary if samples of n = 1,028 were taken over and over? Show work. (1 pt) E. What would be the shape of the sampling distribution for the sample mean? Explain (1 pt) E. would a sample mean of $907 or more be a very surprising result if in fact, -3899 and = $250? Hint: Use Excel to find P(X > 907) (1 pt) $885 and -S2507(1 F would a sample mean of $907 or more be a very surprising result if in fact pt) G. Since we do not know , we can apply the Empirical Rule to the sampling distribution for in the following way. Double the standard deviation that you found in part D and subtract that amount from the sample mean to get a lower bound. Add that amount to the sample mean to get an upper bound. Report the interval that you have constructed. This interval gives us a range of plausible values for (1 pt) H. How do the values $899 and $885 compare to this interval? (2 pts)
Explanation / Answer
Please answer parts D-H ! According to a Gallup poll conducted in October 2017, Americans planned to spend $907 orn Christmas gifts, an increase of $121 over the previous year. Results for this Gallup poll were based on telephone interviews conducted Oct. 5-11,2017, with a random sample of 1,028 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia. A. Is $907 a parameter or a statistic? Explain. (1 pt) B. For this study identify the population of interest, sample selected and parameter of interest. (1 pt) Let denote the true mean amount that was expected to be spent on Christmas gifts among those in the population and let represent the standard deviation of these amounts. C. Is it possible that the sample mean was $907 even if turned out to be $899? what if was equal to $885? What about $1000? (1 pt) D. Assume that -$250, what does the Central Limit Theorem say about how the sample mean would vary if samples of n = 1,028 were taken over and over? Show work. (1 pt) E. What would be the shape of the sampling distribution for the sample mean? Explain (1 pt) E. would a sample mean of $907 or more be a very surprising result if in fact, -3899 and = $250? Hint: Use Excel to find P(X > 907) (1 pt) $885 and -S2507(1 F would a sample mean of $907 or more be a very surprising result if in fact pt) G. Since we do not know , we can apply the Empirical Rule to the sampling distribution for in the following way. Double the standard deviation that you found in part D and subtract that amount from the sample mean to get a lower bound. Add that amount to the sample mean to get an upper bound. Report the interval that you have constructed. This interval gives us a range of plausible values for (1 pt) H. How do the values $899 and $885 compare to this interval? (2 pts)