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- 1. Calculate r2 2. Interpret r2 in the context of this research. How large is this effect (small, medium, large)? 3. Make an statistical decision about the null using alpha =.05. Will you reject or retain the null based on your data? 4. Provide a conclusion of the data using Descriptive statistics and the context of the research.Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level. The null and alternative hypothesis would be: Но : им — ИF Ho: Им — Иr Но: им — Ar Ho: Pм — Pr Ho:Pм — Pr Ho:рм — Pғ µf Ho:PM PF Ho:PM = PF Ho:PM H1: µM > µF H1:µM + HF H1:µM PF The test is: left-tailed right-tailed two-tailed Based on a sample of 20 men, 25% owned cats Based on a sample of 80 women, 35% owned cats The test statistic is: (to 2 decimals) (Hint: difference in proportions, not z) The positive critical value is: (to 2 decimals) (Hint: the proportion, not z) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesisA researcher administers a treatment to a sample of participants selected from a population with µ = 90. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? a. a sample mean much different than 80 with α = .01 b. a sample mean much different than 80 with α = .05 c. a sample mean near 80 with α = .01 d. a sample mean near 80 with α = .05
- A researcher wanted to determine if car preference was related to city of birth. So, she polled 200 people who were born in either Detroit or Tokyo and asked them which car manufacturer they preferred. The data are below. Conduct the appropriate χ2 statistical test using an alpha level of .05 and the eight steps of hypothesis testing. (NOTE: You do not have to use the correction equation if df=1) Chevy Toyota Detroit 75 25 Tokyo 15 85Suppose there is a claim that a certain population has a mean, 4, that is different than 9. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis, Ho, and the alternative hypothesis, H1, as follows. Hg: 4= 9 H: u=9 Suppose you also know the following information. The value of the test statistic based on the sample is -2.044 (rounded to 3 decimal places). The p-value is 0.041 (rounded to 3 decimal places). (a) Complete the steps below for this hypothesis test. Standard Normal Distribution 04 Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed 0.3+ Step 2: Enter the test statistic. (Round to 3 decimal places.) 0.2+ Step 3: Shade the area represented by the p-value. 0.1+ Step 4: Enter the p-value. (Round to 3 decimal places.) ? (b) Based on your answer to part (a), which statement below is true? O since the p-value is less…Which of the following is not a cause of perfect multicollinearity? Select all that apply. One of the explanatory variables is equal to half of another explanatory variable for 100% of the observations in the sample. The correlation between two of the explanatory variables is 1.00. One of the explanatory variables is equal to half of another explanatory variable for 20% of the observations in the sample. A dummy variable for male is included at the same time as a dummy variable for non-male. One of the regressors is X and another regressor is X².
- 12State the Result: A hypothesis test was conducted at the alpha = 0.01 level of significance. The test resulted in a p-value of 0.044.Test the claim that the proportion of men who own cats is larger than 20% at the .05 significance level. The null and alternative hypothesis would be: 0.2 Но:р — 0.2 Но: и 0.2 Ho:H Ho:H H:р + 0.2 Н]:р 0.2 Hi:р > 0.2 Hi:р#0.2 0.2 Но:р || The test is: left-tailed two-tailed right-tailed Based on a sample of 25 people, 25% owned cats The test statistic is: (to 2 decimals) The critical value is: (to 2 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis
- Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .10 significance level. The null and alternative hypothesis would be: Но: дм — Мр Но: рм — МF Но: рм — Pr Но: рм — рF Но: им — МЕ Но: рм — РF PF Ho:HM = µf Ho:PM = Pf H1: µM + HF H1:µM PF H1:µM > µF H1:PM < PF The test is: left-tailed right-tailed two-tailed Based on a sample of 60 men, 35% owned cats Based on a sample of 40 women, 55% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: Fail to reject the null hypothesis Reject the null hypothesisTest the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.02 significance level. The null and alternative hypothesis would be: Но: HF Ho: UM = µF Ho:PM — pF Ho:рм PF Ho: им — MF Ho:; PF Нi: рм > иF Hi: рм # pF Hi:рм рF Hi: рм < pF Hi:рм # pғ The test is: right-tailed two-tailed left-tailed Based on a sample of 80 men, 25% owned cats Based on a sample of 40 women, 50% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesisSuppose there is a claim that a certain population has a mean, µ, that is different than 7. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis H, and the alternative hypothesis H, as follows. Hoi u= 7 H: u =7 Suppose you also know the following information. The critical values are - 1.960 and 1.960 (rounded to 3 decimal places). The value of the test statistic is 2.477 (rounded to 3 decimal places). (a) Complete the steps below to show the rejection region(s) and the value of the test statistic for this test. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. One-tailed 0.3 Two-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) 0.2+ 0.1+ Step 3: Enter the test statistic. (Round to 3 decimal places.) 2 (b) Based on your answer to part (a), choose the correct statement. O The value of the test…