Exam 13: Hypothesis Testing: Comparing Two Populations

A university lecturer claims that students who attend lecturers score a higher final mark in her course than students who watch the lecture recordings online. The lecturer takes a random sample of the final marks of 40 students who attended her university lectures and found their average mark was 65 with a standard deviation of 5. The lecturer takes a random sample of 30 university students who watched the lecture recordings online and found their average mark was 60 with a standard deviation of 8. Is there significant evidence to support this university lecturer's claim? Test at the 5% level of significance, assuming that the population variances are unequal.

In testing the hypotheses: H0: p1 - p2 = 0 HA: p1 - p2 ≠ 0, we found the following statistics: n1 = 350, x1 = 178. n2 = 250, x2 = 112. What conclusion can we draw at the 5% significance level?

A sample of size 100 selected from one population has 53 successes, and a sample of size 150 selected from a second population has 95 successes. The test statistic for testing the equality of the population proportions is equal to:

Ten functionally illiterate adults were given an experimental one-week crash course in reading. Each of the 10 was given a reading test prior to the course and another test after the course. The results are shown below. Adult 1 2 3 4 5 6 7 8 9 10 Score after course 48 42 43 34 50 30 43 38 41 30 Score before course 31 34 18 30 44 28 34 33 27 32 Is there enough evidence to infer at the 5% significance level that the reading scores have improved?

A survey of 1500 Queenslanders reveals that 945 believe there is too much violence on television. In a survey of 1500 Western Australians, 810 believe that there is too much television violence. Can we infer at the 1% significance level that the proportions of Queenslanders and Western Australians who believe that there is too much violence on television differ?

A sample of size 100 selected from one population has 60 successes, and a sample of size 150 selected from a second population has 95 successes. The test statistic for testing the equality of the population proportions is equal to:

The managing director of a breakfast cereal manufacturer believes that families in which both spouses work are much more likely to be consumers of his product than those with only one working spouse. To prove his point, he commissions a survey of 300 families in which both spouses work and 300 families with only one working spouse. Each family is asked whether the company's cereal is eaten for breakfast. The results are shown below. Two spouses working One spouse working Eat cereal 114 87 Do not eat cereal 186 213 Do these data provide enough evidence at the 1% significance level to infer that the proportion of families with two working spouses who eat the cereal is at least 5% larger than the proportion of families with one working spouse who eats the cereal?

A politician regularly polls her electorate to ascertain her level of support among voters. This month, 652 out of 1158 voters support her. Five months ago, 412 out of 982 voters supported her. At the 1% significance level, can she claim that support has increased by at least 10 percentage points?

When testing the difference between two population proportions, a t test may be used.

In testing the difference between the means of two normally distributed populations, the number of degrees of freedom associated with the unequal-variances t-test statistic usually results in a non-integer number. It is recommended that you:

The pooled proportion estimate is used to estimate the standard error of the difference between two proportions when the proportions of two populations are hypothesized to be equal.

In testing the hypotheses: H0: p1 - p2 = 0 HA: p1 - p2 ≠ 0, we find the following statistics: n1 = 200, x1 = 80. n2 = 200, x2 = 140. What conclusion can we draw at the 10% significance level?

A political poll taken immediately prior to a state election reveals that 158 out of 250 male voters and 105 out of 200 female voters intend to vote for the Independent candidate. What is the p-value of the test?

A political analyst in Perth surveys a random sample of Labor Party members and compares the results with those obtained from a random sample of Liberal Party members. This would be an example of:

The marketing manager of a pharmaceutical company believes that more females than males use its acne medicine. In a recent survey, 2500 teenagers were asked whether or not they use that particular product. The responses, categorised by gender, are summarised below. Use acne medicine Do not use acne medicine Female 540 810 Male 391 759 Do these data provide enough evidence at the 10% significance level to support the manager's claim?

Do interstate drivers exceed the speed limit more frequently than local motorists? This vital question was addressed by the Road Traffic Authority. A random sample of the speeds of 2500 randomly selected cars was categorised according to whether the car was registered in the state or in some other state, and whether or not the car was violating the speed limit. The data are shown below. Local cars Interstate cars Speeding 521 328 Not speeding 1141 510 Do these data provide enough evidence to support the highway patrol's claim at the 5% significance level?

A simple random sample of ten firms was asked how much money (in thousands of dollars) they spent on employee training programs this year and how much they plan to spend on these programs next year. The data are shown below. Firm 1 2 3 4 5 6 7 8 9 10 This year 25 31 12 15 21 36 18 5 9 17 Next year 21 30 18 20 22 36 20 10 8 15 Assume that the populations of amount spent on employee training programs are normally distributed. Can we infer at the 5% significance level that more money will be spent on employee training programs next year than this year?

Two independent samples of sizes 40 and 50 are randomly selected from two normally distributed populations. Assume that the population variances are known. In order to test the difference between the population means, µ1 - µ2, which of the following test statistics should be used?

If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on, the samples are referred to as:

Thirty-five employees who completed two years of tertiary education were asked to take a basic mathematics test. The mean and standard deviation of their marks were 75.1 and 12.8, respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test marks were 72.1 and 14.6, respectively. Can we infer at the 10% significance level that a difference exists between the two groups?