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<________ ​(Round to three decimal places as​ needed.)

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 = 15, x=0.45, s=1.02 Reduction in Pain Level After Sham Treatment (2): n = 15, x=0.38, s=1.55 a. Use a 0.01 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? OA. Ho H1 H2 oc Hoi HH2 H₁: H1 H2 B. Ho: H1 H2 H₁₁₂ OD. Ho H1 H2 The test statistic, t, is (Round to two decimal places as needed.)

H0 : =150.00 kPa H1 :>150.00 kPa b) α= 0.01; sample variance : 1300 freq. table  sample deviation : 36.0555 freq. table

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​:…

A company manufactures an electrical cooling fan.  When the fans are performing properly, samples of 200 fans average 12.5 watts with an average range of 1.2 watts.  A 3σ control chart program is being used to monitor the performance of the fans, and these data from the 10 most recent samples were collected:   Sample Number Sample Mean Sample Range 1 12.5 1.1 2 12.45 1.2 3 12.55 0.9 4 12.50 0.8 5 12.45 0.9 6 12.60 1.0 7 12.48 1.4 8 12.46 1.1 9 12.56 0.9 10 12.48 0.8    Compute the 3σ control limits and center line for an ⁻x chart. Compute the 3σ control limits and center line for an R chart. Plot the sample data on the ⁻x and R charts and decide if the performance of the fan is in control.

How do you find (b.)?

The following data represent the results from an independent-measures study comparing two treatment conditions. Treatment   I II 10 7 N = 16 8 4 G = 120 7 9 ∑X² = 1036 9 3   13 7   7 6   6 10   12 2   M = 9.000 M = 6.000   T = 72 T = 48   SS = 44 SS = 56     Use an independent-measures t test with α = .05 to determine whether there is a significant mean difference between the two treatments. (Use three decimal places; subtract MIIII from MII.) t-critical = ±   t =       t Distribution Degrees of Freedom = 21             -3.0-2.0-1.00.01.02.03.0t   Conclusion: Fail to reject the null hypothesis; there are significant differences between the two treatments.   Reject the null hypothesis; there are significant differences between the two treatments.   Fail to reject the null hypothesis; there are no significant differences between the two treatments.   Reject the null hypothesis; there are…

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…