Question

1.Which of the following would be an appropriate alternative hypothesis?

A.The population proportion is more than 0.44

B.The sample proportion is at most 0.44

C.The population proportion is at most 0.44

D.The sample proportion is more than 0.44

2.A sample of 100 fuses from a very large shipment is found to have 10 that are defective. The 95% confidence interval of defective fuses is

A.0.0412 to 0.1588

B.0.8412 to 0.9588

C.0.8941 to 0.9059

D.0.0941 to 0.1059

3. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is not 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is – 2.20. Can we conclude that H0 should be rejected at the (i) 10%, (ii) 5%, and (iii) 1% level of significance?

A.(i) yes; (ii) yes; (iii) yes

B.(i) no; (ii) no; (iii) no

C.(i) no; (ii) no; (iii) yes

D.(i) yes; (ii) yes; (iii) no

4.When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that the population proportion is estimated to be, the __________ the sample size required

A.The effect cannot be determined from the information given

B.larger

C.The sample size is not affected

D.smaller

Answer 1

1. Hypothesis testing is done to draw an estimate of population parameters. While establishing alternative hypothesis we use greater than or less than. So answer should be A.

2. This is a binomial distribution which can be approximated to normal.

mean=n*p= 100*(1/10)= 10

variance= n*p*(1-p)=100*(1/10)*(9/10)=9

std devation=3

confidence interval= [10-(1.96*3), 10+(1.96*3)] = [4.12, 15.88]

proportion = [4.12/100,15.88/100]= [0.0412,0.1588]

3. H0: p=9/10

H1: p 9/10

this is a two tailed test.

critical values at different levels of significance

0.1 : 1.65

0.05 : 1.96

0.01 : 2.58

test statistic lies beyond the critical value only at 0.01 significance. So, H0 can be rejected only in this case.

answer is no,no,yes

4. larger