According to previous research, the mean amount of money spent on gifts for the holiday season by a working adult is $1500. With the current prices in Trickidad, a young researcher believes that this amount has been increased. She takes a random sample of 60 working adults and collects data on the amount of money they have spent on gifts for the current holiday season, giving a mean of $1650. Assume that the population standard deviation for the amount of money spent on gifts for the holiday season by a working adult is $150 and that this amount of spending is normally distributed. (a) Construct a 95% confidence level for the mean amount of money spent on gifts for the holiday season by a working adult. Interpret your answer. (b) Is there any evidence at 5% level of significance to suggest that the mean amount of money spent on gifts for the holiday season by a working adult has increased? Use the critical value approach in arriving at your conclusion showing clearly all the required steps. (c) Determine the p-value for this hypothesis test and show how the same conclusion can be arrived at as in ‘(b)’ above. Note: There is no need to duplicate some of the steps taken in ‘(b)’ above.
QUESTION 4
According to previous research, the mean amount of money spent on gifts for the holiday season by a
working adult is $1500. With the current prices in Trickidad, a young researcher believes that this
amount has been increased.
She takes a random sample of 60 working adults and collects data on the amount of money they have
spent on gifts for the current holiday season, giving a mean of $1650.
Assume that the population standard deviation for the amount of money spent on gifts for the holiday
season by a working adult is $150 and that this amount of spending is
(a) Construct a 95% confidence level for the mean amount of money spent on gifts for the holiday
season by a working adult. Interpret your answer.
(b) Is there any evidence at 5% level of significance to suggest that the mean amount of money
spent on gifts for the holiday season by a working adult has increased? Use the critical value
approach in arriving at your conclusion showing clearly all the required steps.
(c) Determine the p-value for this hypothesis test and show how the same conclusion can be
arrived at as in ‘(b)’ above. Note: There is no need to duplicate some of the steps taken in ‘(b)’
above.
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