4. (This problem is required to submit) Consider the following hypothesis test. H:µ = 20 H.:µ + 20 A sample of 200 items will be taken and the population standard deviation is o = 10. Use a = 0.05. Compute the probability of making a Type II error if the population mean is: a. u =18.0 (33%) (Note: without calculation process, no credit) b. µ= 22.5(33%) (Note: without calculation process, no credit) c. µ=21.0 (34%) (Note: without calculation process, no credit)
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- You wish to test the following claim (HaHa) at a significance level of α=0.01You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:μ=58.2Ho:μ=58.2 Ha:μ>58.2Ha:μ>58.2You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=27n=27 with mean M=65.4M=65.4 and a standard deviation of SD=9.9SD=9.9.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 58.2. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 58.2. The sample data…You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ=59.9 Ha:μ<59.9You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=4n=4 with mean M=38.6M=38.6 and a standard deviation of SD=10.9SD=10.9.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 59.9. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 59.9. The sample data support the claim that the…
- Consider a large population with?=67 and ?=6. Assuming ?/?≤0.05, find the mean and standard deviation of the sample mean, x ,a. for a sample of size 21 ux= ox= b. For a sample of size 62 ux= ox=You wish to test the following claim (Ha) at a significance level of a=0.02. H0: u=83.9 Ha:u<83.9 You believe the population is normally distributed but you do not know the standard deviation. You obtain a sample of size n=119 with the meanM=79.4 and a standard deviation of SD=12.9. What is the test statistic foe this sample? What is the P value for this sample? The p value is less than or greater than a? This test statistic leads to a decision to: reject the null, accept the null, or fail to reject the null?You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005. Ho:μ=85.9Ho:μ=85.9 Ha:μ>85.9Ha:μ>85.9 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=6n=6 with mean M=89.6M=89.6 and a standard deviation of SD=9.1SD=9.1. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =
- You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005. Ho:μ=77.3Ho:μ=77.3 Ha:μ≠77.3Ha:μ≠77.3You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=18n=18 with mean M=84M=84 and a standard deviation of SD=10.6SD=10.6.What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =You wish to test the following claim (HaHa) at a significance level of 0.10. Ho:μ=80.1Ho:μ=80.1 Ha:μ<80.1Ha:μ<80.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=11n=11 with mean M=70.3M=70.3 and a standard deviation of SD=7.7SD=7.7. The test statistic is -4.221 What is the p-value for this sample?You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ=81.9 Ha:μ≠81.9You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=12n=12 with mean M=72.6M=72.6 and a standard deviation of SD=7.5SD=7.5.What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = ______The p-value is... A.) less than (or equal to) αα B.) greater than α This p-value leads to a decision to... A.) reject the null B.) accept the null C.) fail to reject the null As such, the final conclusion is that... A.) There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 81.9. B.) There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 81.9. C.) The sample data support the claim that the population mean is not equal to 81.9. D.) There is not sufficient sample evidence to…
- If the t-statistic for a single sample t-test is 1.58, what can you conclude? a. The test is significant at an alpha level of .05. b. The sample size of the test was at least 30. c. The sample mean was larger than the population mean. d. The population standard deviation was smaller than the difference between the sample mean and the population mean.You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:μ=84.9Ho:μ=84.9 Ha:μ>84.9Ha:μ>84.9You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=25n=25 with a mean of M=89.9M=89.9 and a standard deviation of SD=10.4SD=10.4.What is the critical value for this test? (Report answer accurate to three decimal places.)critical value = IncorrectWhat is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = IncorrectThe test statistic is... in the critical region not in the critical region Incorrect This test statistic leads to a decision to... reject the null accept the null fail to reject the null Incorrect As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 84.9. There is not sufficient evidence to warrant rejection of the…