Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment​ (with magnets) group and the sham​ (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below.     Treatment Sham   μ μ1 μ2 n 16 16 x 0.55 0.36 s 0.84 1.49 a.  Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.   What are the null and alternative​ hypotheses?     A. H0​: μ1=μ2 H1​: μ1≠μ2   B. H0​: μ1=μ2 H1​: μ1>μ2   C. H0​: μ1<μ2 H1​: μ1≥μ2   D. H0​: μ1≠μ2 H1​: μ1<μ2 The test​ statistic, t, is The​ P-value is State the conclusion for the test.       Fail to reject Reject the null hypothesis. There     is not is sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. Is it valid to argue that magnets might appear to be effective if the sample sizes are​ larger?   Since the   sample mean sample standard deviation for those treated with magnets is     greater than less than equal to the sample mean for those given a sham​ treatment, it     is not is valid to argue that magnets might appear to be effective if the sample sizes are larger. b. Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.   <μ1−μ2<

You wish to test the following claim (Ha) at a significance level of a = 0.001. H.:µ1 = µ2 Ha:µ1 # µ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal (So use the "pool" option). You obtain the following two samples of data. Sample #1 Sample #2 86.4 60.5 63.3 93.5 94.6 61.1 99.2 55.9 85.8 107 88.9 68.8 88.3 61.9 78.8 59.2 103.8 99.7 74.3 72.5 76.5 62 70.5 80.7 80.2 59.2 64.3 107 89.3 113.2 48.5 95.2 72.1 76.1 115.5 75.1 97.6 88.4 96.4 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? For this calculation, use the P-value reported from the "2-sample t- test" from the technology you are using. (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a greater than a This test statistic leads…

Male BMI Female BMI se H2 47 Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. n 47 26.3343 27.3646 8.781948 se 5.636805 se What are the null and alternative hypotheses? se O B. Ho H1 = H2 H1 H1 #H2 O A. Ho H1 H2 H1: H1 H2 O D. H, H1 #H2 H1: H1 < H2 se The test statistic, t, is. (Round to two decimal places as needed.) se The P-value is (Round to three decimal places as needed.)

Researchers were interested in the impact of texting on student learning. A group of 99 college students received texts from the researcher during a prerecorded psychology lecture. At the end of the 20-minute lecture, students answered a 17-question quiz about the material that had just been presented; scores were compared to a population mean of 15 on the test, though the population standard deviation was unknown. Which statistical test should the researchers use to analyze their data? a. dependent-samples t test b. one-sample t test c. independent-samples t test d. z test

Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog​ scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) to​ (c) below.   Reduction in Pain Level After Magnet Treatment ​(μ1​): n=29​, x=0.58​, s=0.95 Reduction in Pain Level After Sham Treatment ​(μ2​): n=29​, x=0.48​, s=1.56       Question content area bottom Part 1 a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment​ (similar to a​ placebo).   What are the null and alternative​ hypotheses?     A. H0​: μ1≠μ2 H1​: μ1<μ2   B. H0​: μ1<μ2 H1​:…

An online math tutor service would like to claim that the average time spent taking a standardized test after students go through tutoring is less than the average time spent before going through tutoring. A simple random sample of students takes a pre-test, then goes through tutoring and takes a post-test. Results of the sample are shown below. Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Confidence Level Before After 82.333 74.944 110.118 199.820 18 0.727 18 0 17 -3.227 0.002 -1.740 0.005 -2.110 99% What are the population parameters? Pick Is the two-sample hypothesis test a paired t-test or an unpaired t-test? Pick What is the level of significance? Ex: 0.12 What is the null hypothesis? Ho: Mafter Pick Mbefore What is the alternative hypothesis? Ha : Pafter Pick Should Ho be rejected or does Ho fail to be rejected? Pick What conclusion can be drawn from the data? Pick…

Choose the appropriate statistical test. When computing, be sure to round each answer as indicated. A dentist wonders if depression affects ratings of tooth pain. In the general population, using a scale of 1-10 with higher values indicating more pain, the average pain rating for patients with toothaches is 6.8. A sample of 30 patients that show high levels of depression have an average pain rating of 7.1 (variance 0.8). What should the dentist determine? 1. Calculate the estimated standard error. (round to 3 decimals). [st.error] 2. What is thet-obtained? (round to 3 decimals). 3. What is the t-cv? (exact value) 4. What is your conclusion? Only type "Reject" or Retain"

In this problem, we use your critical values table to explore the significance ofr based on different sample sizes. Critical Values for Correlation Coefficient r a = 0.05 =0.01 „A=0.05 a = 0.01 a = 0.05 a = 0.01 3. 1.00 1.00 13 0.53 0.68 23 0.41 0.53 4. 0.95 0.99 14 0.53 0.66 24 0.40 0.52 0.88 0.96 15 0.51 0.64 25 0.40 0.51 6. 0.81 0.92 16 0.50 0.61 26 0.39 0.50 0.75 0.87 17 0.48 0.61 27 0.38 0.49 8. 0.71 0.83 18 0.47 0.59 28 0.37 0.48 9. 0.67 0.80 19 0.46 0.58 29 0.37 0.47 10 0.63 0.76 20 0.44 0.56 30 0.36 0.46 11 0.60 0.73 21 0.43 0.55 12 0.58 0.71 22 0.42 0.54

A company that develops an automated customer service model is interested in knowing whether two versions, Version A and Version B, will get different ratings from customers. Participants in a focus group are taken through samples from both versions, then take a survey to rate each version. A summary of the data obtained from the study is given below. Assume ratings from the different surveys generally have the same standard deviation. Mean Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Confidence Level Version A Version B 33.133 28.67 15 15 -0.325 0.00 14 n = Ex: 9 -1.426 0.088 -1.345 0.176 -1.761 95% Degrees of freedom: df Point estimate for Version A: XA = Ex: 1.234 Point estimate for Version B: x B = 1 = من t = −1 Ex: 1.234 0 1 t = P = = Ex: 1.234 2 3 2

Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog​ scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) to​ (c) below.   Reduction in Pain Level After Magnet Treatment ​(μ1​): n=27​, x=0.46​, s=0.89 Reduction in Pain Level After Sham Treatment ​(μ2​): n=27​, x=0.42​, s= 1.43   * Find the t stat * Find the p value * state the conclusion * Does the confidence interval support the conclusion of the test * Does it appear that magnets are effective in treating back​ pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are​ larger? * Is it valid to argue that magnets might appear to be…