Question

In Exercises 1-2, (a) identify the claim and state H0 and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

1. A meteorologist claims that the median daily high temperature for the month of July in Pittsburgh is 83 Fahrenheit. The high temperatures (in degrees Fahrenheit) for randomly selected July days in Pittsburgh are listed below. At α=0.01, is there enough evidence to reject the meteorologist’s claim?

74 79 81 86 90 79 81 83 81 74 78 76 84 82 85

2. A financial services institution claims that the median amount of credit card debt for families holding such debts is at least $2300. In a random sample of 104 families with credit card debt, the debts of 60 families were less than $2300 and the debts of 44 families were greater than $2300. At α=0.02, can you reject the institution’s claim?

Answer 1

Ans:

1)

sample mean=80.867

s=4.438

n=15

Test statistic:

t=(80.867-83)/(4.438/SQRT(15))

t=-1.861

df=15-1=14

critical t value=tinv(0.01,14)=2.977

Fail to reject the null hypothesis.

There is not sufficient evidence to reject the meteorologist’s claim.