p = alpha A) reject the null hypothesis B) accept the null hypotheses
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It is given that
P-value p ≤ α ( significance level )
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- 19% of all college students volunteer their time. Is the percentage of college students who are volunteers smaller for students receiving financial aid? Of the 343 randomly selected students who receive financial aid, 48 of them volunteered their time. What can be concluded at the αα = 0.01 level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: (please enter a decimal) H1:H1: (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly lower than 19% at αα = 0.01, so there is insufficient evidence to conclude that the percentage of financial aid recipients who volunteer is lower than 19%. The data suggest the populaton…14% of all college students volunteer their time. Is the percentage of college students who are volunteers different for students receiving financial aid? Of the 363 randomly selected students who receive financial aid, 40 of them volunteered their time. What can be concluded at the αα = 0.01 level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: (please enter a decimal) H1:H1: (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly different from 14% at αα = 0.01, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 14%. The data suggest the populaton…Only 17% of registered voters voted in the last election. Will voter participation decline for the upcoming election? Of the 391 randomly selected registered voters surveyed, 47 of them will vote in the upcoming election. What can be concluded at the αα= 0.01 level of significance?For this study, we should use The null and alternative hypotheses would be: H0:H0:(please enter a decimal) H1:H1:(Please enter a decimal)The test statistic = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 4 decimal places.)The p-value is ααBased on this, we should the null hypothesis.Thus, the final conclusion is that ... The data suggest the populaton proportion is significantly lower than 17% at αα= 0.01, so there is statistically significant evidence to conclude that the the percentage of all registered voters who will vote in the upcoming election will be lower than 17%.The data suggest the population proportion is not significantly lower than 17% at αα= 0.01, so…
- Suppose a group of 700 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 223 patients who received the antidepressant drug, 81 were not smoking one year later. Of the 477 patients who received the placebo, 80 were not smoking one year later. Given the null hypothesis H0:(pdrug−pplacebo)=0H0:(pdrug−pplacebo)=0 and the alternative hypothesis Ha:(pdrug−pplacebo)≠0Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.03α=0.03,Suppose a group of 1000 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 383 patients who received the antidepressant drug, 122 were not smoking one year later. Of the 617 patients who received the placebo, 106 were not smoking one year later. Given the null hypothesis H0: (pdrug−pplacebo)=0 and the alternative hypothesis Ha: (pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.05, (a) The test statistic is (b) The P-value is (c) The final conclusion is A. There seems to be evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group. B. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.A recent study at a university showed that the proportion of students who commute more than 15 miles to school is 25%. Suppose we have good reason to suspect that the proportion is greater than 25%, and we carry out a hypothesis test. State the null hypothesis H, and the alternative hypothesis H, that we would use for this test. Ho: 0 H;: D OWhich of the following are the appropriate null and alternative hypothesis? Η := 157, ΗΑ :# 157 Η : μ = 157, HA : μ 145 Η : μ = 157, HA : μ > 157 Η : μ = - 145, HA : μ < 145A blind taste test is conducted to determine which of two colas, Brand A or Brand B, individuals prefer. Individuals are randomly asked to drink one of the two types of cola first, followed by the other cola, and then asked to disclose the drink they prefer. Results of the taste test indicate that 45 of 100 individuals prefer Brand A. Complete parts a through c. ..... (a) Conduct a hypothesis test (preferably using technology) Ho: p= Po versus H,: p# Po for po = 0.34, 0.35, 0.36, ., 0.54, 0.55, 0.56 at the a = 0.05 level of significance. For which values of po do you not reject the null hypothesis? What do each of the values of po represent? Do not reject the null hypothesis for the values of po between (Type integers or decimals as needed.) and inclusively. (b) Construct a 95% confidence interval for the proportion of individuals who prefer Brand A. The lower bound is The upper bound is (Round to three decimal places as needed.) (c) Suppose you changed the level of significance in…A blind taste test is conducted to determine which of two colas, Brand A or Brand B, individuals prefer. Individuals are randomly asked to drink one of the two types of cola first, followed by the other cola, and then asked to disclose the drink they prefer. Results of the taste test indicate that 58 of 100 individuals prefer Brand A. Complete parts a through c. (a) Conduct a hypothesis test (preferably using technology) H0:p=p0 versus H1:p≠p0 for p0=0.47,0.48,0.49,...,0.67,0.68,0.69 at the α=0.05 level of significance. For which values of p0 do you not reject the null hypothesis? What do each of the values of p0 represent? Do not reject the null hypothesis for the values of p0 between _ and _,inclusively.20% of all college students volunteer their time. Is the percentage of college students who are volunteers larger for students receiving financial aid? Of the 366 randomly selected students who receive financial aid, 77 of them volunteered their time. What can be concluded at the αα = 0.10 level of significance? The null and alternative hypotheses would be: H0:H0: p = __?__ (please enter a decimal) H1:H1: p > __?__ (Please enter a decimal) The test statistic z = __?__ (please show your answer to 3 decimal places.) The p-value = __?__(Please show your answer to 4 decimal places.)Consider the following table in reference to a hypothesis test: Ho True Ho false (1) (3) Accept Ho Reject Ho (2) (4) A Type I error occurs if entry (3) occurs. 1) True 2) False
