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The provided sample variance is and the sample size is given by
Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a Chi-Square test for one population variance will be used.
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- Assume that the data values in this problem come from independent populations and that each population follows a normal distribution.Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds).4.14 4.24 4.24 3.58 3.55 3.82 4.08 4.37 3.92 3.82 4.17 3.10 4.89 2.93 4.98 3.34Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.3238.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. OA. Ho: H₁ H₂ H₁: ₁2₂ OC. Ho: #₁ #₂ H₁: HyThe dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a=0.10, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 10.4 8.2 8.8 12.6 13.1 6.1 9.90 11.3 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and H₂? Ο Α. Ho: με 11.0 H₂>11.0 O D. Ho: 11.0 H: ≤11.0 A O A. Fail to reject Ho because the P-value is greater than the significance level. OB. Reject H, because the P-value is greater than the significance level. OC. Reject Ho because the P-value is less than the significance level. OD. Fail to reject Ho because the P-value is less than the significance level. (d) Interpret the decision in the context of the original claim. O A.…Upright vacuum cleaners have either a hard body type or a soft body type. Shown are the weights in pounds of a sample of each type. At =α0.10 , can it be concluded that the means of the weights are different? Assume the variables are normally distributed and the variances are unequal. Hard body types Soft body types 21 24 17 12 15 15 20 14 20 16 16 17 17 18 17 24 23 13 13 15 16 18 18 17 17 Use μ1for the mean weight of the hard body type.Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.7 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 810 samples is 6.6 ppm. Assume the variance is known to be 1.00. Does the data support the claim at the 0.02 level? Step 1 of 5: Enter the hypotheses: Answer 2 Points E Keypad Keyboard Shortcuts Họ: Prev Ne: © 2020 Hawkes Learning MacBook Air 80 888 DII DD F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 ! @ %23 & 1 2 3 4 %3D Q W E T Y { P A S D F G H J K C M ? on command command option .. .- V - * 00 B.The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a = 0.01, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 12.1 8.9 11.8 8.4 7.2 10.1 12.1 8.7Researchers 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:…Suppose that weights of college mathematics textbooks in the United States are normally distributed with mean µ = 2.25 lbs and variance σ2 = 0.2025 lbs. Find the weight that corresponds to Q3 and interpret this measure of position in the context of the problem.An employment information service claims the mean annual salary for senior level product engineers is $95,000. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At α=0.05, test the claim that the mean salary is $95,000. Complete parts (a) through (e) below. Assume the population is normally distributed. Annual Salaries: 100,683 96,363 93,511 112,615 82,435 74,211 77,041 80,894 102,398 76,130 104,053 104,040 91,094 82,028 85,015110,258 Identify the claim and state H0 and Ha. H0:___ ___ ____ Ha: ___ ___ ____ (Type integers or decimals. Do not round.) The claim is the________(alternative or null) hypothesis. Use technology to find the critical value(s) and identify the rejection region(s). The critical value(s) is/are t0= ____ , _____ (Use a comma to separate answers as needed. Round to two decimal places as needed.) The standardized test statistic is T=_______________________________…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…Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.6 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 14 samples is 4.9 ppm with a variance of 1.2 Does the data support the claim at the 0.01 level? Assume the population distribution is approximately normal. Step 2 of 5 : Find the value of the test statistic. Round your answer to three decimal places.A manufacturing company produces bearings. One line of bearings is specified to be 1.64 centimeters (cm) in diameter. A major customer requires that the variance of the bearings be no more than .001 cm². The producer is required to test the bearings before they are shipped, and so the diameters of 16 bearings are measured with a precise instrument, resulting in the following values. Assume bearing diameters are normally distributed. Use the data and a = 0.01 to test to determine whether the population of these bearings is to be rejected because of too high a variance. 1.68 1.62 1.63 1.70 1.66 1.63 1.65 1.71 1.64 1.69 1.57 1.64 1.59 1.66 1.63 1.65 Appendix A Statistical Tables (Round your answer to 2 decimal places, e.g. 15.25.) The value of the test statistic is and we reject the null hypothesis ⇒SEE MORE QUESTIONS
