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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- 2. Five 2 cm thick experimental pieces of an insulation material were tested atrandom. Resulted compression (y) was measured recorded for the given amount ofmeasured pressure. The data are listed below:Pressure Compression1 12 23 24 35 5Fit a simple linear model relating compression y to the applied pressure x and find:a) error variance.b) the coefficient of correlation.An electronic company's records show that the mean number of circuit.boards rejected per batch is 5.7 with a variance of 1.4. Due to a change in the molding process, factory management has hired you to perform a hypothesis test to check if the variance, o, has increased. To do so, you test a random sample of 10 batches produced using the new process; the number of circuit boards rejected per batch has a sample variance of 2.5. Under the assumption that the number of circuit boards rejected per batch using the new process follows a normal distribution, you will perform a chi-square test. Find x, the value of the test statistic for your chi-square test. Round your answer to three or more decimal places. * = 0A 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 A) 3.6 B) 1.8 C) 0.45
- The following information is available for two samples selected from independent normally distributed populations. Population A: n1=30 S2/1=25 Population B: n2=30 S2/2=36 a. Which sample variance do you place in the numerator of FSTAT? b. What is the value of FSTAT?The accompanying data table contains chest deceleration measurements (in g, whereg is the force of gravity) from samples of small, midsize, and large cars. Shown are the technology results for analysis of variance of this data table. Assume that a researcher plans to use a 0.05 significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test. Complete parts (a) and (b) below. Click the icon to view the table of chest deceleration measurements A Click the icon to view the table of analysis of variance results. ..... a. What characteristic of the data specifically indicates that one-way analysis of variance should be used? O A. There are three samples of measurements. O B. The population means are approximately normal. O C. The measurements are categorized according to the one characteristic of size. O D. Nothing specifically indicates that one-way analysis of variance should be used. b. If the objective is to test…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 = 21An 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?The Tukey-Kramer procedure is used for which of the following purposes?A. Test for differences in pairwise means.B. Test for normality of residuals.C. Test for independence of errors.D. Test for homogeneity of variances.
- 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 follow. Test the hypothesis that the mean weight of the two sheets is equal (μ1−μ2μ1−μ2)against the alternative that it is not (and assume equal variances). Find the t-stat to 3 decimal places.Q1. The following data are from a completely randomized design. Treatment A B C 155 148 128 147 152 126 165 124 138 145 140 140 150 152 140 Sample mean 152.4 143.2 134.4 Sample variance 63.8 139.2 46.8 (A). What is the F test statistics value? (B). Compute the mean squares due to error. (C). At the α = 0.01, test whether the means for the three treatments are equal. Using F table, what is the most possible range of values of the p-value? [Multiple choice with single answer] (a) 0.025<p-value<0.1 (b) 0.01<p-value<0.05 (c) 0.01<p-value<0.025 (d) 0.025<p-value<0.05 (e) 0.05<p-value<0.1 (f) None of the aboveA 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.