Question

Suppose that an Internal Revenue Service (IRS) representative claims that the average tax deduction for medical care is $1,250, and assume that this variable is normally distributed. A taxpayer who believes that the deduction might be less than $1,250 decides to randomly sample 12 families who have an average deduction of $934 with a standard deviation of $616. a. What are the null and alternative hypotheses? b. What is the value of the test statistic, i.e. t-stat, in this example? Show your work. c. What is the p-value associated with this test statistic? (HINT: you have less than 30 observations so you will need to use t-table to obtain critical values.) d. What can you conclude at the 10-percent level of significance? What can you conclude at the 5-percent level of significance? Explain. (HINT: you have less than 30 observations so you will need to use t-table to obtain critical values.)

Answer 1

Explanation:

We have bar x = 934

S = 616

n = 12

A.

Null hypothesis: h0: u = 1250

Alternative hypothesis: h1: u< 1250

B. To get the t test statistic

T = 934-1250/616/√12

T = -316/616/3.4641

= -316/117.824

= -1.777

C. O value = p(t<-1.777)

This gives 0.0516

D. At 10% significance

O.0516<0.1 so we reject the null hypothesis and conclude that this deduction is < than 1250

At 5% level of significance

O.o516>0.05. we do not reject the null hypothesis. We conclude there is insufficient evidence of claim being less than 1250