MTH3003 SECOND SEMESTER SESSION 2013/2014 TUTORIAL 8 1.
The variance price of all college textbooks was RM 81 last year. A recent sample of 20 college textbooks produced a variance price equals to RM 87.56. One of college lecturers claims that the current variance price of all college textbooks is greater than RM 81. Assume that the prices of all college textbooks have a normal distribution. The significance level is 1%.
2.
(a)
State the null and alternative hypotheses.
(b)
Obtain the critical value.
(c)
Determine the value of the test statistics.
(d)
Does the data provide sufficient evidence to support the claim?
A sample of 18 observations selected from a normally distributed population produced a sample variance of 4.6. (a)
Write the null and alternative hypotheses to test whether the population variance is different from 2.2.
(b)
Using α = 0.05, find the critical value of
. Show the rejection and non-rejection
regions on a chi-square distribution curve.
3.
(c)
Find the value of the test statistic
.
(d)
Using the 5% significance level, will you reject the null hypothesis stated in part a?
A medical researcher wishes to see whether the variances of the heat rates (in beats per minutes) of smokers are different from the variances of heart rates of people who do not smoke. The two samples are selected and the data are shown below. Smoker
Non-smoker
(a)
Using
, is there enough evidence to support the claim?
(b)
Find a 95% confidence interval for the ratio of the two population variances. Does this interval confirm your conclusion from part (a)? Explain.
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4.
A comparison of the precisions of two machines developed for extracting juice from oranges is to be made using the following data: Machine A
(a)
Machine B
Is there sufficient evidence to indicate that there is a difference in the precision of the two machines at 5% level of significance?
(b)
Find a 95% confidence interval for the ratio of the two population variances. Does this interval confirm your conclusion from part (a)? Explain.
5.
A researcher wanted to study the relationship between gender and owning cell phone. She took a sample of 2000 adults and obtained the information given in the following table. She then conducted a test to see whether gender and owing a cell phone are related.
6.
Own cell phones
Do not own cell phone
Men
640
450
Women
440
470
(a)
State the null and alternative hypothesis for this test.
(b)
Find the critical value and rejection region for
(c)
Find the value of the test statistic.
(d)
Conduct the test and state the conclusion.
One hundred auto drivers who were stopped by the police for some violation were also checked to see if they were wearing seat belts. Records of the results were given in the following table. Wearing seat belt
Not wearing seat belt
Men
34
21
Women
32
13
Test at the 2.5% significance level whether gender wearing seat belt are independent.
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