Question

For the following questions, identify the type of test that should be used. Simply use the corresponding letter: A) One-sample z test (for a mean); B) One-sample t-test; C) One-sample z-test for a proportion (or a chi-squared goodness-of-fit); D) Chi-square goodness of fit (and a z-test is not appropriate); E) Two-sample z-test for a difference between proportions (or a chi-squared test for independence); F) Chi-square test for independence (and a z-test is not appropriate); G) Simple regression; H) Multiple regression; I) Two-independent samples t-test (with homogeneity of variance); J) Two-independent samples t-test (without homogeneity of variance);       K) Two-related samples t-test; L) One-way (independent measures) ANOVA; M) One-way Repeated measures ANOVA; N) Two-way ANOVA (independent, mixed, or repeated measures); O) Mann-Whitney; P) Wilcoxon; Q) Kruskal-Wallis; R) Friedman; If you are going down the interval/ratio branch, it is safe to use parametric measures, unless something is directly stated that clearly indicates otherwise, or unless the data strongly and unambiguously indicates otherwise. Similarly, it is safe to assume homogeneity of variance unless it is clearly indicated otherwise. Do not try to analyze whether or not the experiment is tenable or practical or flawless. This is not your concern right now. Almost all of the below were written by students in this class.

4.         A manufacturer claims that only 5% of the goods he produces are defective. Zoe takes a sample of 500 products and finds that 45 are defective.

5.         Tegan wants to know if there 10C or 10B is the harder class or are they equally hard. She gets a sample of eight students who took both classes and records what score they got on the 10B final, and she then records what the same students got on the 10C sample.

     10B:                 50                     70                     100                   120                   140                   115                   85                     85

    10C:                 92                     72                     109                   82                     138                   136                   88                     67        

6.         A professor wants to know if more boys are likely to speak out in class or whether girls are more likely to speak out in class.

Answer 1

4)

Correct answer: C) One-sample z-test for a proportion (or a chi-squared goodness-of-fit);

Explanation: Since we are comparing one sample proportion with the hypothesized population mean, one-sample z-test for a proportion will be used.

One-sample z-test for a proportion

The null and alternative are,

The z-statistic is computed as follows,

5)

Correct answer: K) Two-related samples t-test;

Explanation: Here the same experiment tested for two experiment conditions. The test score is measured twice for a same student hence this is a two-related samples t-test where the two sample of student test score are taken and compared.

The null and alternative are,

The z-statistic is computed as follows,

Where, D is the difference of test score of students

6)

Correct answer: Two-independent samples t-test (with homogeneity of variance);

Explanation: Since the mean score of the number of times of speak out are being compare for two samples (girls and boys) assuming the variances are equal, the two sample t test will be performed.

The Null and Alternative Hypotheses are,

The t-statistic is computed as follows,