Two independent samples are selected at random from two normal populations, where the unknown population variances are assumed to be equal. The sample statistics are as follows: Assume that a two-tailed hypothesis test is conducted at n₁=20,x=40,s₁=18,n₂=10,x₂=34 and $₂=16. S α = .05, what is the upper critical value? a. t = 2.0484 b. z = 1.96 c. t = 1.7011 d. z = 1.65 e. t = 1.562
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A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks Given :
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A: (b) Degrees of freedom = min(n1-1, n2-1) = min(12-1, 10-1) = 9
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- You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. Ho:μ=80.5Ho:μ=80.5 Ha:μ≠80.5Ha:μ≠80.5You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=13n=13 with mean M=82.3M=82.3 and a standard deviation of SD=9.1SD=9.1. can you help me do this problem on a ti 84? I got help with doing it but did not get the answer letting me know if this can be done on a ti 84 and to help walk me through it.thank youUse the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance a, and sample sizes n, and n2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). Ha H >H2; a = 0.05, n, = 14, n = 13 (a) Find the critical value(s) assuming that the population variances are equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)You wish to test the following claim (Ha) at a significance level of α=0.002α=0.002. Ho:μ=68.9Ho:μ=68.9 Ha:μ>68.9Ha:μ>68.9You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=17 with mean M=74.7 and a standard deviation of SD=13.3.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... A.) less than (or equal to) αα B.) greater than αα This test statistic 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 greater than 68.9. B.) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than…
- You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. Ho:μ=61.3Ho:μ=61.3 Ha:μ>61.3Ha:μ>61.3You 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=67.9M=67.9 and a standard deviation of SD=11.5SD=11.5.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 61.3. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 61.3. The sample data…You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:μ=61.7Ho:μ=61.7 Ha:μ>61.7Ha:μ>61.7You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=23n=23 with a mean of M=67.1M=67.1 and a standard deviation of SD=6.5SD=6.5. use excelWhat is the critical value for this test? (Report answer accurate to three decimal places.)critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = The test statistic is... in the critical region not in the critical region 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 61.7. There is not sufficient evidence to warrant rejection of the claim that the population mean is…You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:μ=51.3Ho:μ=51.3 Ha:μ≠51.3Ha:μ≠51.3You 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=49.2M=49.2 and a standard deviation of SD=5.5SD=5.5.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = CorrectWhat is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = Incorrect0.2128 or 0.2127The p-value is... less than (or equal to) αα greater than αα Correct This test statistic leads to a decision to... reject the null accept the null fail to reject the null Correct As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 51.3. There is not sufficient evidence to warrant rejection of the claim that the population mean is…
- A sample of n=30n=30 data values randomly selected from a normally distributed population has variance s2=18.2s2=18.2. Construct a 99% confidence interval for the population variance. Round your endpoints to one decimal place.You wish to test the following claim (H) at a significance level of a = 0.005. H₂:1 = μ₂ Ha: M1 M₂ You believe both populations are normally distributed, but you do not know the standard deviations for either. However, assume that the variances of the two populations are equal. You obtain a sample of size n₁ = 20 with a mean of ₁ = 60.9 and a standard deviation of SD₁ = 6.2 from the first population. You obtain a sample of size n₂ = 15 with a mean of 2 = 76.9 and a standard deviation of SD2 = 18.6 from the second population. 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... O less than (or equal to) a Ogreater than aYou wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:μ=64.2Ho:μ=64.2 Ha:μ<64.2Ha:μ<64.2You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=8n=8 with a mean of ¯x=53.9x¯=53.9 and a standard deviation of s=8.1s=8.1.What is the critical value for this test? (Report answer accurate to three decimal places.)critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to... reject the null hypothesis accept the null hypothesis fail to reject the null hypothesis As such, the final conclusion is that... There is enough evidence to show that the population mean is not less than 64.2. There is not enough evidence to show that the population mean is not less than 64.2. There is enough…
- You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:μ=58.8Ho:μ=58.8 Ha:μ>58.8Ha:μ>58.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=298n=298 with mean M=59.6M=59.6 and a standard deviation of SD=7.3SD=7.3.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 =In order to compare the means of two normal populations with equal variances, independent random samples are taken of sizes n = 12 and n2 8. The results from the sample data yield: Sample 1 Sample 2 sample mean = 52 sample mean = 48 S1= 1.1 52 = 2.4 To test the null hypothesis Ho: H1 - H2 = 0 versus the alternative hypothesis H, H1- 2 0 at the 0.01 level of significance, the most accurate statement is O The value of the test statistic is 5.08 and the critical value is +2.552 O The value of the test statistic is 2.8 and the critical value is +2.552 O The value of the test statistic is 2.8 and the critical values are -2.552 and +2.552 O The value of the test statistic is 5.08 and the critical value is +2,528 O The value of the test statistic is 5.08 and the critical value is 2.326You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:μ=81.6Ho:μ=81.6 Ha:μ<81.6Ha:μ<81.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=638n=638 with mean M=81M=81 and a standard deviation of SD=11.3SD=11.3.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 81.6. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 81.6. The sample data support the…