According to a Gallup poll conducted in October 2017, Americans planned to spend
ID: 3058074 • Letter: A
Question
According to a Gallup poll conducted in October 2017, Americans planned to spend $907 on 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.
B. Would a sample mean of $907 or more be a very surprising result if in fact, µ = $899 and = $250? Hint: Use Excel to find P (X bar > 907).
C. Would a sample mean of $907 or more be a very surprising result if in fact µ = $885 and = $250?
D. Since we do not know we can apply the Empirical Rule to the sampling distribution of the sample mean in order to find a range of plausible values for . We proceed 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 µ.
E. How do the values $899 and $885 compare to this interval? Is this consistent with your answers to part B and part C?
The fígure below shows an Excel worksheet that computes normal probabilities for you. Use this example to answer the problem on the next page 1 Mean 2 St Dev 2 4 X Value S P(XK 9) 6 P(X>9 9 0.841345| NORM.DIST(B4, B1, B2, TRUE) 0.1586551-NORMDIST(B4, Bl, B2, TRUE) 8 9 10 11 12 From X Value To XValue P(XExplanation / Answer
According to a Gallup poll conducted in October 2017, Americans planned to spend $907 on 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.
B. Would a sample mean of $907 or more be a very surprising result if in fact, µ = $899 and = $250? Hint: Use Excel to find P (X bar > 907).
C. Would a sample mean of $907 or more be a very surprising result if in fact µ = $885 and = $250?
D. Since we do not know we can apply the Empirical Rule to the sampling distribution of the sample mean in order to find a range of plausible values for . We proceed 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 µ.
E. How do the values $899 and $885 compare to this interval? Is this consistent with your answers to part B and part C?
The fígure below shows an Excel worksheet that computes normal probabilities for you. Use this example to answer the problem on the next page 1 Mean 2 St Dev 2 4 X Value S P(XK 9) 6 P(X>9 9 0.841345| NORM.DIST(B4, B1, B2, TRUE) 0.1586551-NORMDIST(B4, Bl, B2, TRUE) 8 9 10 11 12 From X Value To XValue P(XRelated Questions
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