Question

1. Individuals filing federal income tax returns prior to March 31 received an average refund of $1,086. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $930. Based on prior experience a population standard deviation of  = $1,800 may be assumed. What is the p-value (to 4 decimals)? _________

d. Using  = .05, what is the critical value for the test statistic (to 3 decimals)? _________

2. Consider the following hypothesis test:

H0:  ≤ 29
Ha:  > 29

A sample of 50 provided a sample mean of 30.4. The population standard deviation is 6.

b. What is the p-value (to 4 decimals)? ___________

Answer 1

1. b) Here,

sample mean

population standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

Now,

The value of test statistic

P-value =

or, P-value = 0.0830364 (ans)

d) At 5% level of significance,

the critical value for the test statistic is

2. To test against

Here,

sample mean

population standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

Now,

The value of test statistic

P-value

or. P-value = 0.04948 (ans)