Question

1. You would like to test whether more than 50% of U.S. college students are happy with the college they chose. A random sample of 275 U.S. college students contain 142 who are happy with the college they chose.    What would the p-value be to two decimal places.

2. A sociologist believes that people spend over 50 hours per week on the Internet. A random sample of 300 people gives us an average of 51.2 hours on the Internet per week with a standard deviation of 16 hours. What would be the p-value for this hypothesis test? Please round to two decimal places.

3.A random sample of 180 bicycles contains 27 that are red. You want to test the claim that the proportion of bicycles that are red is over .14. What is the p-value to two decimal places?

4. Test the claim that the mean number of M&Ms in a small package is 35. A random sample of 88 small packages of M&Ms gives a mean of 32.5 with a standard deviation of 10. Give the p-value to two decimal places.

Answer 1

1)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.5164 - 0.5)/sqrt(0.5*(1-0.5)/275)
z = 0.54

P-value Approach
P-value = 0.29

2)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (51.2 - 50)/(16/sqrt(300))
t = 1.3

P-value Approach
P-value = 0.1

3)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.15 - 0.14)/sqrt(0.14*(1-0.14)/180)
z = 0.39

P-value Approach
P-value = 0.35

4)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (32.5 - 35)/(10/sqrt(88))
t = -2.35

P-value Approach
P-value = 0.02