the one-sample z-test, the null hypothesis states that: Group of answer choices the population mean is greater than the sample mean the sample mean is greater than the population mean the sample mean is equal to the population mean the sample variance is equal to the population variance
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- Waiting times (in minutes) of customers in a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the mean and median for each of the two samples, then compare the two sets of results. Single Line 6.3 6.6 6.7 6.8 6.9 7.3 7.6 7.7 7.7 7.7 Individual Lines 4.2 5.2 5.9 6.2 6.5 7.7 7.7 8.7 9.4 9.8 ... The mean waiting time for customers in a single line is minutes.Test the indicated claim about the means of two populations. Assume that the two samples are randomly selected, independent, the population standard deviations are not know and not considered equal. Two types of cereal ? are test for their consumption time (in minutes). At the 0.01 significance level, test the claim that the two populations of cereal have equal means. Cereal A Cereal B n1 = 37 n2 = 35 xˉx̄1 = 19.6 min xˉx̄2 = 19.1 min s1 = 1.7 min s2 = 0.6 min What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)H0: Select an answer p₁ x̄₁ μ₂ p̂₁ x̄₂ μ μ(A) p s₁² p₂ σ₁² μ₁ ? > ≥ ≤ < = ≠ Select an answer μ(B) p₁ p p₂ x̄₂ μ x̄₁ s₁² μ₂ μ₁ p̂₁ σ₁² H1: Select an answer σ₂² μ₂ x̄₁ p̂₂ p₁ μ₁ s₂² x̄₂ μ μ(A) p₂ p ? > = ≠ ≥ ≤ < Select an answer p₁ p μ₂ s₁² μ₁ x̄₁ p̂₁ p₂ μ(B) σ₁² μ x̄₂ Original Claim = Select an answer H₁ H₀ df = Based on the hypotheses, find the following: Test Statistic = (Round to three decimal…Treatment Placebo A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.10 significance level for both parts. H2 39 34 2.35 2.69 0.94 0.67 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? O A. Ho: H1=Hz H1: H1> H2 O B. Ho: H1Consider an experiment with four groups, with five values in each. For the ANOVA summary table shown to the right, fill in all the missing results. Degrees of Sum of Mean Source Freedom Squares Square (Variance) c-1=? SSA = ? Among groups Within Source Among groups c-1= Within groups n-c= Total n-1= (Simplify your answers.) groups Total Complete the ANOVA summary table below. Degrees of Freedom n-c=? SSW = 176 n-1=? SST = ? Sum of Squares SSA= SSW = 176 SST= Mean Square (Variance) MSA=33 MSW = MSA=33 MSW = ? F FSTAT= F FSTAT = ?Dala on the eights (Ib) o the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Diet Regular H2 27 27 0.79037 lb 0.80399 lb 0.00449 Ib 0.00756 lb UA. Ho P1= P2 B. Ho H1 7 µ2 D. Ho H1= H2 O C. Ho: H1 =H2 H1: 1 > H2 Hyi HyAn educational psychologist studies the effect of frequent testing on retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. Frequent Quizzes Two Exams n = 20 n = 20 M = 73 M = 68 A. If the first sample variance is s2 = 38 and the second sample has s2 = 42, do the data indicate that testing frequency has a significant effect on performance? Use a two- tailed test at the .05 level of significance. (Note: Because the two sample are the same size, the pooled variance is simply the average of the two sample variances.) tcritical…Treatment Sham Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard H1 H2 23 23 deviations are equal. Complete parts (a) and (b) below. 0.57 0.39 0.62 1.29 a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses? O A. Ho: H1 =H2 O B. Ho: H1 H2 H1: H1Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. At the 0.025 significance level, test the claim that the four brands have the same mean if the following sample results have been obtained. Brand A Brand B Brand C Brand D 21 24 22 17 20 21 18 25 27 29 35 18 23 25 22 25 26 29 29 21 26 36 37Test the claim that the proportion of people who own cats is significantly different than 20% at the 0.1 significance level. The null and alternative hypothesis would be: Ho:p 2 0.2 Ho:p = 0.2 Ho: u 0.2 Ho: u = 0.2 Ho:p 0.2 H1 : p 0.2 The test is: left-tailed two-tailed right-tailed Based on a sample of 700 people, 11% owned cats The p-value is: 0.1 x (to 2 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesisThe estimated standard error of the mean for a relevant sampling distribution provides an indicator of: The average or standard amount we expect a sample mean to differ from the population mean, if the null hypothesis is true The average or standard amount we expect two study condition means to differ from one another in a repeated measures study design due to chance, if the null hypothesis is true All of these answers are correct The average or standard amount we expect two sample group means to differ from one another in an independent groups study design due to chance, if the null hypothesis is trueWaiting times (in minutes) of customers in a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the mean and median for each of the two samples, then compare the two sets of results. Single Line 6.5 6.6 6.7 6.8 7.0 7.1 7.4 7.8 7.8 7.8 Individual Lines 4.2 5.5 5.8 6.1 6.3 7.8 7.8 8.5 9.4 10.1 The mean waiting time for customers in a single line is nothing minutes. The median waiting time for customers in a single line is nothing minutes. The mean waiting time for customers in individual lines is nothing minutes. The median waiting time for customers in individual lines is nothing minutes. Determine whether there is a difference between the two data sets that is not apparent from a comparison of the measures of center. If so, what is it?Analysis of Variance On the following random samples of social class, test the null hypothesis that neighborhood does not vary by social class (note: Higher scores indicate greater neighborliness). 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