stats help
Find the appropriate rejection regions for the large-sample test statistic z in these cases. (a) A left-tailed test at the 10% significance level. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) 2 > 1.645 x z 2.33 x z 30 O HO: [4 = 30 versus Ha: [4 30 u! Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) z: pvalue = State your conclusion. O The p-value is greater than alpha, so H0 is not rejected. There is sufcient evidence to indicate that the mean is different from 30. The p-value is greater than alpha, so H0 is not rejected. There is insufcient evidence to indicate that the mean is different from 30. O The p-value is less than alpha, so H0 is rejected. There is insufficient evidence to indicate that the mean is different from 30. O The pvalue is less than alpha, so H0 is rejected. There is sufcient evidence to indicate that the mean is different from 30. Many companies are becoming involved in flextime, in which a worker schedules his or her own work hours or compresses work weeks. A company that was contemplating the installation of a flextime schedule estimated that it needed a minimum mean of 7 hours per day per assembly worker in order to operate effectively. Each of a random sample of 60 of the company's assemblers was asked to submit a tentative flextime schedule. If the mean number of hours per day for Monday was 6.6 hours and the standard deviation was 2.4 hours, do the data provide sufficient evidence to indicate that the mean number of hours worked per day on Mondays, for all of the company's assemblers, will be less than seven hours? Test using a = 0.05. (Round your answers to two decimal places.) 1-2. Null and alternative hypotheses: O Ho: M 7 O Ho: M = 7 versus Ha: M 7 O Ho: M # 7 versus Hai M = 7 3. Test statistic: Z = 4. Rejection region: If the test is one-tailed, enter NONE for the unused region. 2> Z 5.99 O Ho: M = 5.99 versus Ha: M # 5.99 O Ho: M 5.99 O Ho: M + 5.99 versus Ha: M = 5.99 O Ho: M = 5.99 versus Ha: M Z 0.2 O HO: p = 0.2 versus Ha: p 0.2 J (b) Calculate the test statistic and its p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) Z= pvalue = Use the p-value to evaluate the statistical significance of the results at the 1% level. O H0 is rejected since the p-value is not less than 0.01. O H0 is not rejected since the pvalue is less than 0.01. O H0 is rejected since the p-value is less than 0.01. (9 H0 is not rejected since the p-value is not less than 0.01. J (c) Do the data provide sufficient evidence to indicate that p is different from 0.2? 0 Yes, the data provide sufcient evidence to indicate that p is different from 0.2. No, the data do not provide sufficient evidence to indicate that p is different from 0.2. V You may need to use the appropriate appendix table or technology to answer this question. Need Help? _ An experimenter has prepared a drug-dose level that he claims will induce sleep for at least 80% of people suffering from insomnia. After examining the dosage we feel that his claims regarding the effectiveness of his dosage are inflated. In an attempt to disprove his claim, we administer his prescribed dosage to 40 insomniacs and observe that 29 of them have had sleep induced by the drug dose. Is there enough evidence to refute his claim at the 5% level of significance? State the null and alternative hypotheses. O Ho: p 0.80 O Ho: p 0.80 O Ho: P # 0.80 versus Ha: p = 0.80 Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) test statistic rejection region Z > State your conclusion. O Ho is rejected. There is insufficient evidence to refute the experimenter's claim. O Ho is not rejected. There is sufficient evidence to refute the experimenter's claim. O Ho is rejected. There is sufficient evidence to refute the experimenter's claim. O Ho is not rejected. There is insufficient evidence to refute the experimenter's claim. You may need to use the appropriate appendix table or technology to answer this question. Need Help? Read ItAn experiment was conducted to test the effect of a new drug on a viral infection. After the infection was induced in 100 mice, the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection, and the second group received the drug. After a 30-day period, the proportions of survivors, p, and p2, in the two groups were found to be 0.38 and 0.62, respectively. (a) Is there sufficient evidence to indicate that the drug is effective in treating the viral infection? Use a = 0.05. State the null and alternative hypotheses. O Ho: (P1 - P2) 0 O Ho: (P1 - P2) = 0 versus Ha: (P1 - P2) > 0 O Ho: (P1 - P2) = 0 versus Ha: (P1 - P2) * 0 O Ho: (P1 - P2) # 0 versus Ha: (P1 - P2) = 0 O Ho: (P1 - P2) = 0 versus Ha: (P1 - P2) 7 State your conclusion. O Ho is not rejected. There is sufficient evidence to indicate that the drug is effective in treating the viral infection. O Ho is not rejected. There is insufficient evidence to indicate that the drug is effective in treating the viral infection. O Ho is rejected. There is insufficient evidence to indicate that the drug is effective in treating the viral infection. O Ho is rejected. There is sufficient evidence to indicate that the drug is effective in treating the viral infection. (b) Use a 95% confidence interval to estimate the actual difference (p, - p2) in the survival rates for the treated versus the control groups. (Round your answers to two decimal places.) toIn the last few years, many research studies have shown that the purported benefits of hormone replacement therapy (HRT) do not exist, and in fact, that hormone replacement therapy actually increases the risk of several serious diseases. A four-year experiment involving 4472 women was conducted at 35 medical centres. Half of the women took placebos and half took a prescription drug, a widely prescribed type of hormone replacement therapy. There were x1 = 43 cases of dementia in the hormone group and X2 = 22 in the placebo group. 15 there sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug? Test at the 1% level of significance. (Round your answers to two decimal places.) 1-2. Null and alternative hypotheses: O HO: (p1 p2) 0 versus Ha: (p1 p2) = 0 O HO: (p1 p2) = 0 versus Ha: (p1 p2) 0 Ho: (p1 p2) = 0 versus Ha: (p1 p2) > 0 O Ho: (p1 p2) = 0 versus Ha: (p1 p2) 0 3. Test statistic: z = 4. Rejection region: If the test is one-tailed, enter NONE for the unused region. Z > Z t 5 O Ho: M = 5 versus Ha: M # 5 O Ho: M = 5 versus Hai M t 26 3. Test statistic: t = 4. Rejection region: If the test is one-tailed, enter NONE for the unused region. t> 5. Conclusion: O Ho is rejected. There is sufficient evidence to indicate that the pretreatment mean is less than 26. O Ho is rejected. There is insufficient evidence to indicate that the pretreatment mean is less than 26. O Ho is not rejected. There is insufficient evidence to indicate that the pretreatment mean is less than 26. O Ho is not rejected. There is sufficient evidence to indicate that the pretreatment mean is less than 26. (b) Construct a 95% confidence interval for the true posttreatment mean. (Round your answers to two decimal places.)
