Question

1. A well know Statistical Institution claims that the average College tuition for a law degree costs at least thirty five thousand dollars. Analyzing a sample of fifty law schools in the vicinity of the study we found the sample had a mean tuition of $33,450 with a population standard deviation of $5,978 per year. At 2% level of significance test the Institution's claim.

(a) The hypothesis structure,

(b) The p-value and if you accept or reject the claim (Round the p-value to 4 decimal places)

(c) The conclusion as a verbal statement

2. The store known as PetSmart claims that less than thirty-five percent of Americans own a dog. Analyzing a sample of four hundred Americans, we found that 122 say they own a dog. At the 4% level of significance is there enough evidence to support PetSmart's claim?

(a) The hypothesis structure,

(b) The p-value and if you accept or reject the claim (Round p-value to 4 decimal places)

(c) The conclusion as a verbal statement.

Answer 1

1)

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 35000
Alternative Hypothesis, Ha: μ < 35000

b)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (33450 - 35000)/(5978/sqrt(50))
z = -1.83

P-value Approach
P-value = 0.0336
As P-value >= 0.02, fail to reject null hypothesis.

c)

There is not sufficient evidence to conclude that the average College tuition for a law degree costs at least thirty five thousand dollars.

2)

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.35
Alternative Hypothesis, Ha: p < 0.35

b)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.305 - 0.35)/sqrt(0.35*(1-0.35)/400)
z = -1.89

P-value Approach
P-value = 0.0294
As P-value < 0.04, reject the null hypothesis.

c)

There is sufficient evidence to conclude that less than thirty-five percent of Americans own a dog