Concept explainers
Complete Hypothesis Test. In Exercises 15–22, carry out the following steps.
- a. State the null and alternative hypotheses.
- b. Assuming independence between the two variables, find the expected frequency for each cell of the table.
- c. Find the value of the χ2 statistic.
- d. Use the given significance level to find the χ2 critical value.
- e. Using the given significance level, complete the test of the claim that the two variables are independent. State the conclusion that addresses the original claim.
18. Is the Vaccine Effective? In a USA Today article about an experimental vaccine for children, the following statement appeared: “In a trial involving 1602 children, only 14 (1%) of the 1070 who received the vaccine developed the flu, compared with 95 (18%) of the 532 who got a placebo.” The data are shown in the table below. Use a 0.05 significance level to test for independence between the variable representing treatment (vaccine or placebo) and the variable representing flu (developed flu, did not develop flu). Does the vaccine appear to be effective?
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- Test the claim that the proportion of people who own cats is smaller than 20% at the 0.005 significance level.The null and alternative hypothesis would be: Select One ______ H0:p≤0.2H0:p≤0.2Ha:p>0.2Ha:p>0.2 _______H0:μ≥0.2H0:μ≥0.2Ha:μ<0.2Ha:μ<0.2 _____H0:μ=0.2H0:μ=0.2Ha:μ≠0.2Ha:μ≠0.2 ______H0:p=0.2H0:p=0.2Ha:p≠0.2Ha:p≠0.2 _______H0:p≥0.2H0:p≥0.2Ha:p<0.2Ha:p<0.2 ______H0:μ≤0.2H0:μ≤0.2Ha:μ>0.2Ha:μ>0.2 The test is: Select One ___two-tailed ___left-tailed ___right-tailed Based on a sample of 600 people, 19% owned catsThe test statistic is: __?__ (Round to 2 decimals)The p-value is: __?__ (Round to 2 decimals)arrow_forwardTest the claim that the proportion of people who own cats is smaller than 50% at the 0.025 significance level.The null and alternative hypothesis would be: H0:p≤0.5H0:p≤0.5Ha:p>0.5Ha:p>0.5 H0:μ≥0.5H0:μ≥0.5Ha:μ<0.5Ha:μ<0.5 H0:p=0.5H0:p=0.5Ha:p≠0.5Ha:p≠0.5 H0:p≥0.5H0:p≥0.5Ha:p<0.5Ha:p<0.5 H0:μ=0.5H0:μ=0.5Ha:μ≠0.5Ha:μ≠0.5 H0:μ≤0.5H0:μ≤0.5Ha:μ>0.5Ha:μ>0.5 The test is: right-tailed two-tailed left-tailed Based on a sample of 700 people, 43% owned catsThe test statistic is: (Round to 2 decimals)The p-value is: (Round to 2 decimals)Based on this we: Reject the null hypothesis Do not reject the null hypothesisarrow_forwardTest the null hypothesis H0 : β1 = β2 against the alternative H1 : β1 < β2 at 1% significance level.arrow_forward
- In Exercises, the null hypothesis is H0:µ1 = µ2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required hypothesis test at the 10% significance level. Ha: µ1 ≠ µ2 Observation from Pair Population 1 Population 2 1 13 11 2 16 15 3 13 10 4 14 8 5 12 8 6 8 9 7 17 14arrow_forwardTest the claim that the proportion of people who own cats is larger than 90% at the 0.01 significance level.The null and alternative hypothesis would be: H0:μ=0.9H0:μ=0.9Ha:μ<0.9Ha:μ<0.9 H0:p=0.9H0:p=0.9Ha:p<0.9Ha:p<0.9 H0:μ=0.9H0:μ=0.9Ha:μ>0.9Ha:μ>0.9 H0:p=0.9H0:p=0.9Ha:p>0.9Ha:p>0.9 H0:p=0.9H0:p=0.9Ha:p≠0.9Ha:p≠0.9 H0:μ=0.9H0:μ=0.9Ha:μ≠0.9Ha:μ≠0.9 The test is: left-tailed right-tailed two-tailed Based on a sample of 600 people, 93% owned catsThe test statistic is: (to 2 decimals)The p-value is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forwardIn each of Exercises, we have given the P-value for a hypothesis test. For each exercise, refer to Table to determine the strength of the evidence against the null hypothesis. P-value Evidence against H0 P > 0.10 Weak or none 0.05 < P ≤ 0.10 Moderate 0.01 < P ≤ 0.05 Strong P ≤ 0.01 Very strong P = 0.086arrow_forward
- Consider the following statements: I. As far as the probability of a Type I error is concerned, a two-tailed hypothesis test is more accurate than a one-tailed hypothesis test. II. A point estimation procedure in a one sample scenario utilizes information in a sample to arrive at two points, one positive and one negative in order to estimate the population parameter of interest. a. I and II are both true. b. I and II are both false. c. I is true and II is false. d. I is false and II is true. e. I is false and II is sometimes true.arrow_forwardTest the claim that the proportion of men who own cats is smaller than 70% at the 0.01 significance level. The null and alternative hypothesis would be: H0:μ≥0.7H0:μ≥0.7H1:μ<0.7H1:μ<0.7 H0:p≥0.7H0:p≥0.7H1:p<0.7H1:p<0.7 H0:μ≤0.7H0:μ≤0.7H1:μ>0.7H1:μ>0.7 H0:μ=0.7H0:μ=0.7H1:μ≠0.7H1:μ≠0.7 H0:p≤0.7H0:p≤0.7H1:p>0.7H1:p>0.7 H0:p=0.7H0:p=0.7H1:p≠0.7H1:p≠0.7 Correct The test is: left-tailed right-tailed two-tailed Correct Based on a sample of 300 people, 69% owned cats The test statistic is: (to 2 decimals) The critical value is: (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forwardIn each of Exercises, we have provided a null hypothesis and alternative hypothesis and a sample from the population under consideration. In each case, use theWilcoxon signed-rank test to perform the required hypothesis test at the 10% significance level. H0: µ = 10, Ha: µ<10 7 6 5 12 15 14 13 4arrow_forward
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