We test if the majority of AUM students are females. We collected a sample with sample size 25 and having 20 females. Perform the test with a significance level a = 0.01. Use z0.01 = 2.33, zo.005 = 2.58 (a) State the null and alternative hypothesis and find the test statistic.
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- If a researcher obtained a P-value of 0.01 for a hypothesis test that has a significance level of 0.05, what conclusion should the researcher make? 1 The null hypothesis should not be rejected. 2 The alternative hypothesis should not be rejected. 3 The null hypothesis should be rejected. 4 The alternative hypothesis should be rejected. 5 The null hypothesis must be false.1)Remove the four potential outliers of 0, 0, 8, and 20, and then obtain a new histogram without the outliers. Does the data appear to be normally distributed now? 2)Assuming that the four potential outliers of 0, 0, 8, and 20 are not recording errors, repeat the hypothesis test from part (c) (again setting up the hypothesis test and using either the critical value or p-value approach), and compare your results with that obtained in (c). Did you make a different conclusion? 3)Imagine you know have to make a recommendation/conclusion to the company that hired you: Assuming that the four potential outlies are not recording errors, and looking at the two results above, would you recommend using the first test with the outliers or the second test with the outliers removed? There is no right or wrong answer here, I am interested in what you think and your reasoning.A random sample of 54 students from Cabrillo College are selected from a normal population with mu equal to 20 and sigma equal to 5. After a treatment is administered to the students, the researcher calculated the sample mean to be 21. Is there enough evidence to conclude that the treatment had an effect at the 5% significance level? If the z-statistic equals 1.46 and the critical values are -1.96 and 1.96, what conclusion can we make? (a)reject the null hypothesis and accept the alternative hypothesis (b)cannot determine (c)fail to reject the null hypothesis (d)fail to reject the alternative hypothesis
- Given the information for experiment 1, what is the null hypothesis, standard error, z-critical, and z-observed?A major credit card company is interested in the proportion of individuals who use a competitor’s credit card. Their null hypothesis is H0: p=0.65H0: p=0.65, and based on a sample they find a sample proportion of 0.70 and a pp-value of 0.053. Is there convincing statistical evidence at the 0.05 level of significance that the true proportion of individuals who use the competitor’s card is actually greater than 0.65 ? Yes, because the sample proportion 0.70 is greater than the hypothesized proportion 0.65. A Yes, because the pp-value 0.053 is greater than the significance level 0.05. B No, because the sample proportion 0.70 is greater than the hypothesized proportion 0.65. C No, since the sample proportion 0.70 is exactly 0.05 away from the hypothesized proportion 0.65. D No, because the pp-value 0.053 is greater than the significance level 0.05.3. Continue from the previous question, you are given the following information about y and x. Dependent Variable (y) Independent Variable (x) 5 1 4 2 3 3 2 4 1 5 The point estimate of y when x = 2 is 4. The critical value of t for a two-tailed test with 7 degrees of freedom using α = .05 is 1.943. 2.447. 1.985. 2.365. 5. For a two-tailed hypothesis test with a sample size of 20 and a .04 level of significance, the critical values of the test statistic t are -1.729 and 1.729 -2.093 and 2.093 -2.086 and 2.086 -2.205 and 2.205
- A veterinarian is interested in researching the proportion of men and women cat owners and believes that the proportion of men cat owners is significantly different than the proportion of women cat owners. The veterinarian decides to obtain two independent samples of men and women cat owners and finds from one sample of 80 men, 30% owned cats. In the second sample of 60 women, 55% owned cats. Test the veterinarian's belief at the α=0.05α=0.05 significance level. Preliminary: Is it safe to assume that nmen≤5%nmen≤5% of all men and nwomen≤5%nwomen≤5% of all women? Yes No Verify nˆp(1−ˆp)≥10.np^(1-p^)≥10. Round your answer to one decimal place.nmenˆp(1−ˆp)=nmenp^(1-p^)= nwomenˆp(1−ˆp)=nwomenp^(1-p^)= Test the claim: Determine the null and alternative hypotheses. H0H0: pmenpmen pwomenpwomen HaHa: pmenpmen pwomenpwomen The hypothesis test is left-tailed two-tailed right-tailed Determine the test statistic. Round to two decimal places.x=x= Find the pp-value.…As a researcher for the EPA, you have been asked to determine if the air quality in the UnitedStates has changed over the past 2 years. You select a random sample of 10 metropolitan areasand find the number of days each year that the areas failed to meet acceptable air quality Based on the data, answer the following questions.1. What is the purpose of the study?2. Are the samples independent or dependent?3. What hypotheses would you use?4. What is (are) the critical value(s) that you would use?5. What statistical test would you use?6. How many degrees of freedom are there?7. What is your conclusion?8. Could an independent means test have been used?9. Do you think this was a good way to answer the original question?Assume the critical value on the right side of a Z distribution was 1.96. A researcher received a sample mean that he translated into a z score of 2.5. What decision should the researcher make regarding the null hypothesis?
- Daily anxiety was measured on a scale from 1 (not at all anxious) to 5 (very anxious) in a random sample of 2000 city dwellers from across the U.S. They found that M = 4.13, 95% CIs [4.06, 4.20].How would you interpret these results? What conclusions would you draw about the precision of the point estimate? What statistical decision would have been made in this scenario if the researchers employed Null Hypothesis Significance Testing instead of the New Stats?Suppose a company claims that its market share is less than 16 percent, on average. Several of coworkers do not believe this, so a director decides to do a hypothesis test, at a 1% significance level, to persuade them. He conducts 21 surveys, collects the proper data, and works through the testing procedure: H0: μ≥16; Ha: μ<16 x¯=15.8 σ=1.8 α=0.01 (significance level) The test statistic is z0=x¯−μ0σn√=15.8−161.821√=−0.51 The critical value is −z0.01=−2.33. Conclude whether to reject or not reject H0, and interpret the results. Select the correct answer below: Reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis. Reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean market share is less than 16 percent. Do not reject H0. At the 1% significance level, the test results are not statistically significant…In a hypothesis test with hypotheses H0 :pless than or greater than 0.58 and H1 >0.58 , a random sample of size 1,165 produced a sample proportion of 0.6160. The test is to be made at the 2.5% significance level. What is the value of the test statistic, z, rounded to three decimal places?