Test the hypothesis that the average content of containers of a particular machine oil is 10 liters, if the contents of random sample of 10 containers are: 10.1, 9.3, 9.7, 10.2, 10.1, 9.9, 9.5, 10.2, 9.8, and 10.1. Use 0.01 level of significance. Assume to be normally distributed data.
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Test the hypothesis that the average content of containers of a particular machine oil is 10 liters, if the contents of random sample of 10 containers are: 10.1, 9.3, 9.7, 10.2, 10.1, 9.9, 9.5, 10.2, 9.8, and 10.1. Use 0.01 level of significance. Assume to be
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- a) which for these data is 32.1470, 42.3520, or 10.0674 c) that minimizes the error sum of squares, total sum of squares, or regression sum of squares…for which these data is 32.1470, 42.3520, or 10.0674A researcher takes sample temperatures in Fahrenheit of 17 days from New York City and 18 days from Phoenix. Test the claim that the mean temperature in New York City is different from the mean temperature in Phoenix. Use a significance level of α=0.05. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. New York City Phoenix 99 94.2 95.5 72 93.2 86.8 102 122.1 85.4 114.4 80 94.7 86.4 89.7 75.4 104.7 79.5 77.6 83.4 106.8 64.3 98.6 65.5 91.5 87.7 82 104 97.7 74.3 64.9 59.5 82 82.8 72 116.2 The Hypotheses for this problem are: H0: μ1 = μ2 H1: μ1μ2 Find the p-value. Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. p-value =Suppose a data set from a bike share company contains the number of daily bike rentals at each of 6 stations for the 23 weekdays of a particular month, i.e. we have Yij for i = 1, ..., 23 and j 1,...6. Write down a hierarchical normal model that can be used to estimate the mean number of bike rentals at each station. You can assume that the unknown variance o? of the number of bike rentals is the same for each station.
- 2. Differentiate Independent and Dependent Samples and give an example for each method.Do rats take less time on average than hamsters to travel through a maze? The table below shows the times in seconds that the rats and hamsters took. Rats: 36, 35, 22, 42, 25, 14, 31, 14 Hamsters: 41, 37, 12, 46, 39, 46, 38, 45, 27, 29 Assume that both populations follow a normal distribution. What can be concluded at the a = 0.05 level of significance level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer v Select an answer v Select an answer v (please enter a decimal) H: Select an answer v Select an answer v Select an answer v (Please enter a decimal) b. The test statistic (please show your answer to 3 decimal places.) c. The p-value = (Please show your answer to 4 decimal places.) d. The p-value is ? ♥ a e. Based on this, we should Select an answer f. Thus, the final conclusion is that ... the null hypothesis. O The results are statistically insignificant at a = 0.05, so there is statistically…The heights of men in a certain city are normally distributed with a mean of 275 cm and a variance of 25cm. Compute the minimum height for the top sixteen percent of the men in the city.
- A researcher takes sample temperatures in Fahrenheit of 20 days from Minneapolis and 18 days from Cleveland. Use the sample data shown in the table. Test the claim that the mean temperature in Minneapolis is different than the mean temperature in Cleveland. Use a significance level of α=0.01. Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs. Minneapolis Cleveland 70.1 66.1 69.5 65.9 65.7 61 71.7 62.8 62 67.9 75.3 74.5 63.2 69.1 62 72.5 76.9 80.4 71.3 72.7 70.9 70.4 70.5 76.6 65.1 62.2 76.2 66.1 70.3 86 69.5 81 80.2 68.3 74.3 63.3 70.7 64.6 The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2 Based on these hypotheses, find the following. Round answers to 4 decimal…Do rats take the same amount of time on average than hamsters to travel through a maze? The table below shows the times in seconds that the rats and hamsters took. Rats: 31, 26, 35, 34, 31, 39, 39, 6 Hamsters: 36, 35, 16, 29, 20, 25, 28, 37 Assume that both populations follow a normal distribution. What can be concluded at the a = 0.05 level of significance level of significance? For this studv, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer v Select an answer v Select an answer V (please enter a decimal) H1: Select an answer v Select an answer v v (Please enter a decimal) Select an answer b. The test statistic ?v= (please show your answer to 3 decimal places.) c. The p-value = (Please show your answer to 4 decimal places.) d. The p-value is ? va e. Based on this, we should Select an answer v the null hypothesis. f. Thus, the final conclusion is that ... O The results are statistically insignificant at a = 0.05, so there is…In an investigation of possible brain damage due to alcoholism, an x-ray procedure known as a computer assisted tomography (CAT) scan was used to measure brain densities in 8 chronic alcoholics. For each alcoholic, a nonalcoholic control was selected who matched the alcoholic on age, sex, race, height, and other factors. The brain density measurements on the alcoholics and the matched controls are recorded below. Assume normally distributed data here. Use an appropriate test to determine whether there is evidence of diminished brain density due to chronic alcoholism.
- Women are recommended to consume 1870 calories per day. You suspect that the average calorie intake is larger for women at your college. The data for the 11 women who participated in the study is shown below: 1799, 1703, 2097, 2112, 1824, 1956, 2072, 2113, 1951, 1872, 2126 Assuming that the distribution is normal, what can be concluded at the a = 0.01 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Họ: ?v Select an answer v H: ? vSelect an answer c. The test statistic (please show your answer to 3 decimal places.) d. The p-value = e. The p-value is ? f. Based on this, we should Select an answer g. Thus, the final conclusion is that ... O The data suggest that the population mean calorie intake for women at your college is not significantly more than 1870 at a = 0.01, so there is insufficient evidence to conclude that the population mean calorie intake for women at your college is more than 1870. (Please show your…A movie theater company wants to see if there is a difference in the average price of movie tickets in Chicago and New York City. They sample 20 ticket stubs from Chicago and 25 from New York City. Test the claim using a 1% level of significance. Assume the population variances are unequal and that movie ticket prices are normally distributed. Give answer to at least 4 decimal places. Chicago 9 9 7 11 10 10 8 69 6 0 10 11 11 10' 12 10 9 10 12 8 8 New York City 10 14 10 13 9 14 12 14 12 9 11 12 Mean Variance Observations Hypothesized Mean Difference 284 Test Statistic = p-value = 8 t-Test: Two-Sample Assuming Unequal Variances 14 12 11 13 9 12 7 Check Appver 11 12 14 12 6 Chicago 9.5 2.4736842105263 20 0 df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Choose the correct sign for the alternative hypothesis. 42 Ho: 41 = 42 Η; με ον 112 Based on the hypotheses, find the following: -3.0383993175306 0.00203988 2.4185 0.00407976 2.6981 New York City 11.24…You are testing the claim that having lights on at night increases weight gain (abstract). A sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. Test the claim using a 2% level of significance. Assume the population variances are unequal and that the weight changes are normally distributed. Give answers to 3 decimal places. Data available at StatKey, choose Mice Wgt Gain-2e data set Light (1) 1.71 4.67 4.99 5.33 5.43 6.94 7.15 9.17 10.26 11.67 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem. Ho: ₁ Test Statistic = Dark (₂) 2.27 2.53 2.83 4 4.21 4.6 5.95 6.52 Ha: ₁ Based on the hypotheses, find the following: p-value = = V Select an answer ✓ Select an answer (Hint: difference in means from H₂) The correct decision is to fail to reject the null hypothesis The correct summary…