# Testing of hypothesis

To test if mean utilization of citrus fruits by US people is at least 64%. See attached file for full problem description.

Chpt#7

1)

A citrus grower' s association believes that the mean utilization of fresh citrus fruits by people in US

is a least 94 pounds per year. A ramdon sample fof 103 people in US has amean utilization of fresh citrus of 93.5 pounds

per year and a standard deviation of 30 pounds. At a= 0.02, can you reject the association's claim that the mean utilization

of fresh citrus fruits by people in the US is at least 94 pounds per year?

2)

An auto maker estimates that the mean gas mileage of its luxury sedan is at least 25 miles per gallon.

A random sample of eight such cars had a mean of 23 miles per gallon and a standard deviation of 5 miles per gallon.

At a=0.05 , can you reject the auto maker's claim that the mean gas mileage of its luxury sedan is at least 25 miles per

gallon? Assume the population is normally distributed.

3)

A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first five years of use,.

In a random sample of 57 microwaves five years old, 13% needed repairs. At a=0.04, can you reject the maker's claim that

no more than 10% if its microwaves need repair during the first five years of use?

4)

A state school administrator says the the standard deviation of SAT verbal test scores is 105. A random sample of

14 SAT verbal test scores has a standard deviation of 113. At a=0.01, test the administrator's claim. What can you conclude?

Assume the population is normally distributed.

7.3

Find the critical value for the indicated t-test. Level of significance ÿ and sample size N.

23) Two-tail test, ÿ=0.05, n-20

24) Right-tail test, ÿ=0.01, n=8

25) Left-tail test, ÿ=0.10, n=15

26) Two-tail test,ÿ=0.05, n=12

27) Claim: μœ95, ÿ=0.05, Sample statistics: ˜=94.1,s=1.53,n=12

use t-test to test the claim about the population mean at the given level of significance using the given sample statistics.

Assume the population is normally distributed.

33) A fitness magazine advetises that the average monthly cost of joining a health club is $25. You work for a

customer advocacy group and are asked to test this claim. You find that a random sample of 18 clubs has a mean

monthly cost of $26.25 and a standard deviation of $3.23. At ÿ=0.10, do you have enough evidence to reject

the advertisment claim?

35) A medical association says that the mean number of hours of sleep high school students get each night is at

least 6. The number of hours of sleep a random sample of 20 high school students got in one night is listed. At

ÿ=0.01, can you reject the association's claim?

5.2 6.3 4.2 4.1 8.2 3.5 6.4 9.1 6.2 5.8

7.4 5 4 5.3 4.2 3.1 7.9 8.2 5.3 5.9

37) Claim: p=0.15 ÿ=0.05 sample statistics Þ 0.09, n=40

45) A polling agency says that over 75% of people in US prepare and file their income taxes before April 15th. In a

random survey of 1036 people in the US, 818 said they prepare and file their income taxes before April 15th.

Test the agency's claim at the ÿ=0.10 level. What can you conclude?

46) The Western blot assay is a blood test for the presence of HIV. It has been found that this test sometines gives

false positive results for HIV; especially, when it does not find a certain antibody called p-31 antibody. A medical

researcher claims that the rate of false positives in this case is 2%. A recent study of 121 randomly selected US

blood donors who tested positive for HIV but did not have p-31 antibodies in their blood found that 4 were actually

HIV negative. Test the researcher's claim of a 2% false positive rate at the ÿ=0.05 level. What can you conclude?

7.5 Use χ²-test, find the critical value, for the indicated χ²-test for a population varience, sample sizen, and level significance.

51) Claim:σ²>2; 2;ÿ=0.10. Sample statistics: s²=2.38, n=18

55) A bolt manufacturer makes a type of bolt to be used in airtight containers. The manufacturer needs to be sure that all

its bolts are very similar in width, so it sets an upper tolerance limit for the varience of bolts width at 0.01. A random

sample of 28 bolts yields a variance of 0.064 for bolt width. Test the manufacturer's claim that the variance is at most

0.01 at ÿ=0.005 level. What can you conclude?

#### Solution Summary

The expert tests to mean utilization of citrus fruits by US people is at least 64%.