The data for a random sample of six paired observations are shown in the table. a. Calculate x and s b. Express , in terms of μ, and μ₂. c. Form a 90% confidence interval for H d. Test the null hypothesis Ho: H = 0 against the alternative hypothesis H₂: #0. Use α=0.10. a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Find X- xd=0 (Round to two decimal places as needed.) C Pair 1 2 3 4 5 6 Population 1 Sample (Observation 1) 12 11 6 3 3 Population 2 Sample (Observation 2) 9 9 5 4

The admission office needs your help to evaluate the following hypothesis: Ho: there is not a significant linear relationship between the two sections Against: HA: there is a significant linear relationship between the two sections 1. What is the calculated F statistics? (round to the nearest hundredth) 2. Evaluate the F calculated and indicate if you are going to reject or fail to reject the null hypothesis using an alpha = 0.05 (reject/fail to reject)

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.      Ho:μ1=μ2      Ha:μ1≠μ2You believe both populations are normally distributed and that the population standard deviations are known. You obtain a sample of size n1=42 with a mean of ¯x1=69.5 and a population standard deviation of σ1=16.2 from the first population. You obtain a sample of size n2=55 with a mean of ¯x2=75.4 and a population standard deviation of σ2=17.9 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... 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 first population…

10 for both samples QUESTION 7 A researcher reports t(12) = 2.86, p=.04 for a repeated-measures research study. From this we know: Oa. The researcher would have failed to reject the null if their alpha = .05, and there were 12 participants in the sample. Ob. The researcher would have rejected the null, their alpha = 2.86, and there were 13 participants in the sample. OC. The researcher would have rejected the null if their alpha = .05, and there were 13 participants in the sample. d. The researcher would have failed to reject the null if their alpha = .05, and there were 13 participants in the sample. %3D QUESTION 8 Click Save and Submit to save and submit. Click Save All Answers to save all answers.

Given the following null and alternative hypotheses, conduct a hypothesis test using an alpha equal to 0.05. (Note: The population standard deviations are assumed to be known.) H0: µ1 ≤ µ2 HA: µ1 > µ2 The sample means for the two populations are shown as follows: sample mean 1 = 144,  sample mean 2 = 129 population standard deviation 1 = 11,  population standard deviation 2 = 16 sample size 1 = 40, sample size 2 = 50 Answer:  Decision Rule : Reject H0 if  Zcal > citical value Z =  Test statistic: (Z calculated) Zcal =    (use 4 decimal places)Conclusion:    H0.

Laura asks whether the type of school students attend (private versus public) results in different performance on a test. A sample of N=100 students from a private school produce a mean of 71.30 on a test, and the mean of the population of public school students is µ=75.62 with ?௫ =28. a. Write the alternative hypothesis. b. Write the null hypothesis. c. With α=.05, what is zcrit? d. Compute zobt e. What should Laura conclude?

The NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?

Q1. Which of the following represents Type II error? a. Rejecting the Ho after a test statistic results in a p-value of 0.10 at α =0.05.B. Rejecting the Ho after a test statistic results in a p-value of 0.025 at α=0.05.C. None of the above

12. Two independent samples are taken from two populations. Sample 1 has a mean of 12.8, a standard deviation of 2.3, and a sample size of 18. Sample 2 has a mean of 14.2, a standard deviation of 5.2, and a sample size of 23. This gives a standard error se(Ã1 — Ă2) = 1.212. A 95% confidence interval for the difference between the two means is: (A) (-2.00, -0.80). (B) (11.66, 13.94). (C) (-3.96, 1.16). (D) (-3.85, 1.05). (E) (-3.78, 0.98).

You wish to test the following claim (H1H1) at a significance level of α=0.10α=0.10.      H0:μ=51.8      H1:μ<51.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=19n=19 with mean ¯x=42.4x¯=42.4 and a standard deviation of s=13.2s=13.2.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 or greater than αα This test statistic leads to a decision to... reject the null or accept the null or 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 51.8. or There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 51.8. or The sample…