Question

QUESTION PART A: In a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $35 and standard deviation of $4. Find the margin of error at a 98% confidence level.

Give your answer to two decimal places.

QUESTION PART B: If n=12, ¯xx¯(x-bar)=44, and s=11, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

( , )

Answer 1

Solution:

QUESTION PART A: In a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $35 and a standard deviation of $4. Find the margin of error at a 98% confidence level.

The margin of error is:

Where:

is the critical value at 0.02 significance level for df=n-1=29-1=28

QUESTION PART B: If n=12, ¯xx¯(x-bar)=44, and s=11, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population.

The 95% confidence interval for the estimate of the population mean is:

Where:

is the critical value at 0.05 significance level for df=n-1=12-1=11

Therefore, we have: