(a) At the 1% level whether the sample comes from a population with mean 23.2 hours. (b) At the 5% level whether it comes from a population with mean 20.8 hours. (c) At the 5% level whether it comes from a population with mean less than 20.8 hours
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- Department of Education was analysing the average mathematics test score in the schools in Victoria. It noticed that there were dramatic differences in scores among the schools. In the attempt to improve the scores of all the schools, department attempted to determine the factors that account for the differences. Accordingly, they took a random sample of 40 schools across the state and for each determined the mean test score last year, the percentage of teachers in the schools who have at least one university degree in mathematics, the mean age and the mean annual income of the mathematics teachers. The following is regression output from Excel. SUMMARY OUTPUT Regression Statistics Multiple R 0.597512 R Square 0.357021 Adjusted R Square 0.303439 Standard Error 7.724526 Observations 40 ANOVA df SS MS F Significance F…Let's use SPSS to run a one-sample t-test! Imagine that you are interested in whether the number of hours students in a statistics course work each week differs from the average number of hours reported by the general student body at ASU. Thankfully, you have a data set that consists of information from students in a statistics course, including how many hours they work each week ("workhours"). You also happen to know that the average number of hours worked each week by the general student population at ASU is 25. Use the data provided to conduct a one sample t-test in SPSS comparing the sample data to the population mean.. The dependent variable for your test should be "workhours". Based on your output, the average number of hours worked each week by a sample is ________ . Enter your answer rounded to two decimal places (i.e., 10.01, not 10.1, not 10.0, not 10.010).Restaurant Bill by GenderA study compared the cost of restaurant meals when people pay individually versus splitting the bill as a group. In the experiment half of the people were told they would each be responsible for individual meals costs and the other half were told the cost would be split equally among the six people at the table. In the study, the diners were also chosen so that half the people at each table were female and half were male. We can test for a difference in mean meal cost between females (n1=24, x¯1=44.46, s¯1=15.48) and males (n2=24, x¯2=43.75, s2=14.81).Let group 1 and group 2 be the meal costs for females and males, respectively. state the null and alternative hypotheses calculate the relevant test statistic find the p-value
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- An athletic shoemaker wants to test if their new running shoe specially made for sprinting is better than the competition. To do this, they recruit 35 NCAA sprinters and time their 100-meter dash wearing the company's shoe and then time their 100-meter dash again wearing the competitor’s shoe. The difference of these times is then calculated asTimecompany.shoe−Timecompetitor.shoe. The sample mean difference in times is 0.53 seconds and the sample standard deviation is 1.1. Conduct a hypothesis test at theα=0.1 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in the context of the problem) (b) Calculate the test statistic (c) Calculate the critical value. (d) Draw a picture of the distribution of the test statistic underH0. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at theα= 0.15 level and state your conclusions in the…At a local food processing plant, it used to take an average of 90 minutes for new workers to learn a food processing job. Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean time taken by new workers to learn the food processing procedure on this new machine is different from 90 minutes. A sample of 20 workers showed that it took, on average, 85 minutes for them to learn the food processing procedure on the new machine. It is known that the learning times for all new workers are normally distributed with a population standard deviation of 7 minutes. Use a significance level of 0.01 to test the claim that the mean time is different from 90 minutes. What is the decision? A) Reject Ho because the test statistic is in the critical region and the p-value is greater than the significance level. B) Reject Ho because the test statistic is not in the critical region and the p-value is greater than the significance level.…At a local food processing plant, it used to take an average of 90 minutes for new workers to learn a food processing job. Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean time taken by new workers to learn the food processing procedure on this new machine is different from 90 minutes. A sample of 20 workers showed that it took, on average, 85 minutes for them to learn the food processing procedure on the new machine. It is known that the learning times for all new workers are normally distributed with a population standard deviation of 7 minutes. Use a significance level of 0.01 to test the claim that the mean time is different from 90 minutes. What is the test statistic? A) -7.01 B) -2.539 C) -3.19 D) -2.528 E) -1.96