Two kinds of thread are being compared for strength. The data are as follows: (kg) Brand A: 78.3 s (kg) n 5.6 14 Brand B: 87.2 6.3 17 Calculate the degrees of freedom (always an integer) in determining the rejection region of the null hypothesis, assuming normality and unequal population variances.
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- A math instructor claims that college women have more credit card debt than college men. She conducts a random sample of 38 college men and 32 college women, determines their average credit card debt, and obtains the following statistics in the picture: Test the claim that college women have more credit card debt than college men at the α = .05 level of significance. Assume unequal variances. a. Hypotheses: b. Test Statistic: c. Critical Value(s): d. Decision: e. Conclusion: A horticulturist at a large garden nursery wants to compare two different mist blowers for consistent application. She wants to use the mist blower with the smaller variance, which means more consistent application. She wants to test that the variance of Type A (0.087 gal.2) is significantly greater than the variance of Type B (0.073 gal.2) using a = 0.05. (Ensure you use the following steps: Null hypothesis, Alternative hypothesis, Test statistic, Critical value, Decision with reason, Interpretation). Турe A Туре В si = = 0.087 sz = 0.073 n, = 16 n2 = 21The yield per tract in a certain region of farmland is known to have a populationstandard deviation of 13 bushels. Using the old seed variety, the population mean yield μwas 39 bushels. A farmer tests a new seed variety on a random sample of 36 tracts, andfinds a sample mean yield of 45.2 bushels. Is the population mean yield using the newseed variety different from 39? Use α= 0.10.a. State the null hypothesis . __________________State the alternative hypothesis.____________________b. Find the test statistic. _____ c. Find the P-value for the test. _____________
- Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.4 parts/million (ppm). A researcher believes that the current ozone level is not at the normal level. The mean of 1090 samples is 4.3 ppm. Assume the variance is known to be 1.44. Does the data support the claim at the 0.05 level? Step 1 of 5: Enter the hypotheses: Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places. Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Enter the decision rule. Step 5 of 5: Enter the conclusion.A two-way ANOVA experiment with no interaction is conducted. Factor A has four levels (columns) and Factor B has eight levels (rows). Assume normality in the underlying populations. The results include the following sum of squares terms: SST=367.5 SSA = 207.0 SSE = 52.4 a. Construct an ANOVA table. (Round "SS" and "MS" to 2 decimal places and "F" to 3 decimal places.) ANOVA Source of Variation Rows Columns Error Total SS X Answer is complete but not entirely correct. 207.00 X 108.10 X 52.40 367.50 df 7 3 21 31 MS 29.57 X 36.03 X 2.50 F 11.850 X 14.412 X p- value 0.001 0.000The average score on a statistics test was 2.52 with a standard deviation of 0.75. The teacher suspects that the exam was very difficult; Based on the above, he wants to adjust the scores so that the mean is 3.58 and the standard deviation is 0.25. Compute the values a and b such that the fit of type aX+b provide the desired mean and variance? Calculate: a=?b=?
- An article in Technometrics (1999, Vol. 41, pp.202-211) studied the capability of a gauge by measuring the weights of two sheets of paper. The data are shown below. Test the hypothesis that the two means are equal. Assume equal variances and an alpha-level of 0.05. Answer the following questions regarding your t-test. Paper Observations 1 3.481 3.448 3.485 3.475 3.472 3.477 3.472 3.464 3.472 3.470 3.470 3.470 3.477 3.473 3.474 2 3.258 3.254 3.256 3.249 3.241 3.254 3.247 3.257 3.239 3.250 3.258 3.239 3.245 3.240 3.254 1. What is the calculated t-statistic? (use 4 significant figures) 2. Enter the absolute value of the critical t-value based upon the fact that this is a two-tailed test and that we are using an alpha-level of 0.05? (use 4 significant figures) 3. Based on the comparison between the critical t-value and the calculated t-statistic, will the null hypothesis reject or not reject?A scrap metal dealer claims that the mean of his cash sales is 'no more than R80', but an Internal Revenue Service agent believes the dealer is untruthful. The agent randomly selects a sample of 20 cash customers and find the mean purchase to be R91, with a variance of R441. The test statistic (rounded off to four decimals) is: A. T = 2.3425 B. Z = 2.3425 C. T = 0.0113 D. Z = 0.2381The mean and the variance of a sample of size 16 from normal population are 32 and 8, respectively. For testing the hypotheses H,:0%=46vsH, : 0> # 4.6 thetest statistic is: Select one: O a.22.83 O b.19.57 () ¢.29.35 O d.26.09
- A. 2.1A package of Toys Galore Cereal is marked "Net Wt. 10 oz." The actual weight is normally distributed, with a mean of 10 oz and a variance of 0.16. (a) What percent of the packages will weigh less than 10 oz? %(b) What weight will be exceeded by 2.3% of the packages? (Round your answer to one decimal place.) ozA random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a sample variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal. The value of the test statistic is 1.80 O b. 3.6 С. 0.45 2.