SOLVING_ONE SAMPLE HYPOTHESIS TESTING

Question 1

A manufacturer claims that its rechargeable batteries are good for an average of more than 1,000 charges. A random sample of 100 batteries has a mean life of 1002 charges and a population standard deviation of 14. Is there enough evidence to support this claim at 0.01 level of significance?

Answer 1

Zcritical= 2.33
Zcomputed= 1.4286
Z-test
Conclusion: Do not reject Ho
Ho: u<1000 charges

Question 2

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses salad dressings is working property when 8 ounces are dispensed. Suppose that the average amount dispensed in a particular sample of 35 bottles is 7.91 ounces with a variance of 0.03 ounces squared. Is there evidence that the machine should be stopped and production wait for repairs? The lost production from a shutdown is potentially so great that management feels that the level of significance in the analysis should be 99%.

Answer 2

Zcritical= 2.58
Zcomputed=-3.08
Conclusion: Reject Ho
Ho:u=8oz

Question 3

A local telephone company claims that the average length of a phone call is 8 minutes. In a random sample of 18 phone calls, the sample mean was 7.8 minutes, and the standard deviation was 0.5 minutes. Is there enough evidence to support this claim at
a = 0.05?

Answer 3

tcricital=2.11
df=17
tcomputed= -1.6971
Conclusion: Do not reject Ho
Ho: u= 8 minutes

Question 4

Juan has a mean time of 16.43 seconds for running a 300m dash with a standard deviation of 0.8 seconds. His dad claimed that he can run quicker if he has a new pair of shoes. His dad bought him a shoes and tested it 15 times. For 15 times with the new pair of shoes, Juan’s mean time in running 300m becomes 16 seconds. His dad concluded that the shoes helped him run faster. Is
Juan’s dad conclusion correct? Conduct a hypothesis test if a = 0.05

Answer 4

tcritical=1.76
df=14
tcomputed=-2.08
Conclusion: Reject Ho
Ho: u> 16.43 seconds

Question 5

Statesville college claims that 94% of their graduates find employment within six months of graduation. In a sample of 500 randomly selected graduates, 485 of them were employed. Is there enough evidence to support the college’s claim at 10% level of significance?

Answer 5

Population proportion:
Zcritical= 1.65
Zcomputed= 2.8247
Conclusion: Reject Ho
Ho: p=0.94

Question 6

Suppose a consumer group suspects that the proportion of households that have three or more smartphones is 30%. A smartphone company has reason to believe that the proportion is not 30%. Before they start a big advertising campaign, they conduct a hypothesis test with 90% level of significance. Their marketing people survey 150 households with the result that 43 of the households have three or more cell phones.

Answer 6

Zcritical= 1.65
Zcomputed= -0.267
Conclusion: Do not reject Ho
Ho: p=0.30
Popuation proportion