Exam 14: 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.

Test the following hypotheses at the 5% level of significance: H₀: µ $\mu$ ₁ - µ $\mu$ ₂ = 0 H_A: µ $\mu$ ₁ - µ $\mu$ ₂ < 0, given the following statistics: n₁ = 10, x₁ = 58.6, s₁ = 13.45. n₂ = 10, x₂ = 64.6, s₂ = 11.15. Estimate with 95% confidence the difference between the two population means.

Which of the following best describes the symbol $\bar { x } _ { D }$ ?

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 Don't 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?

Motor vehicle insurance appraisers examine cars that have been involved in accidental collisions to assess the cost of repairs. An insurance executive is concerned that different appraisers produce significantly different assessments. In an experiment, 10 cars that had recently been involved in accidents were shown to two appraisers. Each assessed the estimated repair costs. The results are shown below. Car Appraiser 1 Appraiser 2 1 1650 1400 2 360 380 3 640 600 4 1010 920 5 890 930 6 750 650 7 440 410 8 1210 1080 9 520 480 10 690 770 Can the executive conclude at the 5% significance level that the appraisers differ in their assessments?

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 3 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?

When the necessary conditions are met, a two-tail test is being conducted to test the difference between two population proportions. If the value of the test statistic z is 2.05, then the p-value is:

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 3 Score before course 31 34 18 30 44 28 34 33 27 32 a. Estimate the mean improvement with 95% confidence. b. Briefly describe what the interval estimate in part a. tells you.

A quality control inspector keeps a tally sheet of the numbers of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Production line Acceptable products Unacceptable products 1 152 48 2 136 54 a. What is the p-value of the test? b. Estimate with 95% confidence the difference in population proportions.

In random samples of 25 and 22 from each of two normal populations, we find the following statistics: x₁-bar = 56, s₁ = 8. x₂-bar = 62, s₂ = 8.5. Assume that the population variances are equal. Estimate with 95% confidence the difference between the two population means.

In testing the hypotheses: H₀: p₁ - p₂ = 0 H₁: 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?

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:

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. Can we infer at the 5% significance level that the proportions of male and female voters who intend to vote for the Independent candidate differ?

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?

In testing the hypotheses: H₀: $\mu$ _D = 5 H_A: $\mu$ _D $\neq$ 5, two random samples from two normal populations produced the following statistics: n_D = 36, x_D = 7.8, s_D = 7.5. What conclusion can we draw at the 5% significance level?

Two independent samples of sizes 30 and 35 are randomly selected from two normal populations with equal variances. Which of the following is the test statistic that should be used to test the difference between the population means?

The degrees of freedom for a t test of the difference of population means in a matched pairs experiment is samples is n₁ - 1, because n₁ = n₂.

In testing the difference between the means of two normal populations, using two independent samples, when the population variances are unknown and unequal, the sampling distribution of the resulting statistic is: