In the comparison of two kinds of paint, a consumer testing service finds that four 1-gallon cans of one brand cover on the average 46 square feet with a standard deviation of 31 square feet, whereas four 1-gallon cans of another brand cover on the average 92 square feet with a standard deviation of 26 square feet. Assuming that the two populations sampled are normal and have equal variances, test the null hypothesis u1-42=0 against the alternative hypothesis µ1 - 42 > 0 at the 0.05 level of significance.
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- A manufacture of chocolate chips would like to know whether it's bag filling machine works correctly at the 404 gram setting. It is believed that the machine is under filling the bags. A 27 bag sample had a mean of 402 grams with a variance of 676. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there a sufficient to support the claim that the bags are underfilled? There is or isn't sufficient evident to support this claim that the bags are underfilled?In a random sample of males, it was found that 25 write with their left hands and 217 do not. In a random sample of females, it was found that 58 write with their left hands and 450 do not. Use a .05 significance level to test the claim that the rate of left-handedness among males is less than that among females. Identify the test statistic.z=?In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a significance test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The hypotheses are: H0: μ = 9.4 minutes HA: μ ≠ 9.4 minutesSuppose that the results of the sample lead to non-rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. Choose the best asnwer below: A. Neither B. Type I error C. Type II error D.No error
- Two soap brands have a competition over the longevity of their bars. A sample of 21 bars from company A lasts an average of 13.1 days with a sample variance of 21.2. A sample of 24 bars from company B lasts for an average 10.3 days with a sample variance of 19.3. Test to see if company A’s variance is larger than company B's variance using a 5% level of significance. The null hypothesis is that the variances are the same. The alternate hypothesis is that company A’s variance is larger than company B’s variance. Report your conclusion: a) fail to reject the null hypothesis b) reject the null hypothesisA study was conducted to determine if the performance of a certain type of surgery on young horses had any effect on certain kinds of blood cell types in the animal. Fluid samples were taken from each of six foals an hour after the operation. Suppose that the data on WBC leukocytes follow the normal distribution. One sample Chi-squared test for variancedata: wbcX-squared = 3.5321, df = 5, p-value = 0.3815alternaative hypothesis: true variance is less than 4 Question: Is there evidence to say that the variance of WBC leukocytes is less than 4? State the conclusion based from the results of the test. Choices:- There is no sufficient evidence that the variance of WBC leukocytes is less than 4.- There is a sufficient evidence that the variance of WBC leukocytes is less than 4.Using traditional methods, it takes 8.7 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 12 students and observed that they had a mean of 8.4 hours with a variance of 2.56. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.
- Gestation period is the length of pregnancy, or to be more precise, the interval between fertilization and birth. In Syrian hamsters, the average gestation period is 16 days. Suppose you have a sample of 31 Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups, and who have an average gestation length of 17.1 days and a sample variance of 26.0 days. You want to test the hypothesis that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is sMM= a. 31, b. 0.5232, c. 0.7328, d. 0.9158. The t statistic is- a. 1.50, b. 2.10, c. 2.63, d. 1.20 Now suppose you have a larger sample size n = 95. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same…Two groups of individuals were compared with respect to a high carbohydrate low-fat diet (LF) and a high-fat low carbohydrate diet (LC). Mood was assessed using a total mood disturbance score where a lower score is associated with a less negative mood. Assuming that the random samples come from independent normal distributions with a common but unknown variance, construct a 95% confidence interval for the difference between the two population means, LC less LF. Group LC LF 28+18.56 28±8.96 28±22.37 28+22.30 n 12 13 mean 47.3 19.3 standard deviation 28.3 25.8Two groups of individuals were compared with respect to a high carbohydrate low- fat diet (LF) and a high-fat low carbohydrate diet (LC). Mood was assessed using a total mood disturbance score where a lower score is associated with a less negative mood. Assuming that the random samples come from independent normal distributions with a common but unknown variance, construct a 95% confidence interval for the difference between the two population means, LC less LF. Group LC LF 28+22.37 28+18.56 28+22.30 28±8.96 n 12 13 mean 47.3 19.3 standard deviation 28.3 25.8
- On the basis of data provided by a Romac Salary survey, the variance in annual salaries for seniors in public accounting firms is approximately 2.1 and the variance in annual salaries for managers in public accounting firms is approximately 11.1. The salary data were provided in thousands of dollars. Assuming that the salary data were based on samples of 25 seniors and 26 managers, test the hypothesis that the population variances in the salaries are equal. At a 0.05 level f significance, what is your conclusion? use excel pleaseA researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.