Question

In a survey, 25 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $34 and standard deviation of $2. Construct a confidence interval at a 95% confidence level.

Give your answers to one decimal place.

±±

Interpret your confidence interval in the context of this problem.

Answer 1

df = n - 1 = 25 - 1 = 24

t critical value at 0.05 significance level with 24 df = 2.064

95% confidence interval for is

t * S / sqrt(n)

34 2.064 * 2 / sqrt(25)

34 0.8

The interval is 34-0.8 to 34+0.8

33.2 to 34.8

That is 95% CI is ( 33.2 , 34.8 )

Interpretation- We are 95% confident that true mean is between $33.2 and $34.8