Arandom variable X is normally distributed with a mean of 121 and a variance of 121, and a random variable Y is normally distributed with a mean of 170 and a variance of 289 The random variables have a correlation coefficient equal to 05 Find the mean and variance of the random varlable below W-4X+5Y
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- 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 10% 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 (x₁) 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: Select an answer ? V Select an answer V Ha: Select an answer ✓ Based on the hypotheses, find the following: Test Statistic = Dark (₂) 2.27 2.53 2.83 4 4.21 4.6 5.95 6.52 p-value = ? V Select an answer V (Hint: difference in means from Ha) The correct decision is to Select an answer…Several bakeries in a town were asked the price for different amounts of donuts at their shop. The scatter plot with Total Cost (in dollars) 876543 ~ TO 0 0 1 Donut Pricing 2 3 4 5 Number of Donuts 6 7 8 line of best fit was created from the data gathered. Part A: Estimate the correlation coefficient. Explain your reasoning for the given value. Part B: How many positive and negative residuals are there? Explain your reasoning. Part C: State the point with the largest absolute value residual and interpret the point in terms of the context of the data.A researcher takes sample temperatures in Fahrenheit of 16 days from Miami and 14 days from Atlanta. Use the sample data shown in the table. Test the claim that the mean temperature in Miami greater than the mean temperature in Atlanta. Use a significance level of α=0.10α=0.10.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. Miami Atlanta 68.3 73.6 83.1 69.3 79.1 54.9 72 81.1 72.8 78.6 83.3 54 82.7 36.1 80.7 44.3 87 58.4 83.1 50.8 77.4 60.5 86.1 61.2 76.3 46.8 74.5 54.4 83.3 78.5 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 places. Test Statistic = p-value = The p-value is The correct…
- A company is doing a hypothesis test on the variation in quality from two suppliers. Both distributions are normal, and the populations are independent. Use a = 0.05. A sample of 31 products were selected from Supplier 1 and a standard deviation of quality was found to be 3.77. A sample of 16 products were selected from Supplier 2 and a standard deviation of quality was found to be 3.5659. Test to see if the variance in quality for Supplier 1 is larger than Supplier 2. 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: 0.² H₁: 0.² Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The p-value is = The decision is to [Fail to reject the null hypothesis The correct summary would be: There is not enough evidence to support the claim in quality for Supplier 1 is larger than Supplier 2. o that the varianceA researcher found a significant correlation of .12 between gender (coded as 0 = ‘male’ and 1 = ‘female’) and number of friends at university. If the assigned values of gender were changed to 1 = ‘female’ and 2 = ‘male’, how would this affect the correlation? The strength of the relationship would become weaker The amount of variance explained by the relationship would increase It would become nonsignificantThe sign would change to become negative A researcher is trying to predict anxiety (measured on a 7-point scale) from exposure to stress (operationalised as the number of stressful life events participants can recall in the last week). She has found a correlation coefficient of r = .54 between anxiety and stress, with a standard deviation of 4.45 for anxiety and a variance of 17.21 for stress. What other information is needed to calculate b? The sums of squares of stressThe sums of products of anxiety and stress The covariance of anxiety and stressNo other information is…Records from previous years for a casualty insurance company show that its clients average a combined total of 1.9 auto accidents per day, with a variance of 0.31. The actuaries of the company claim that the current variance, oʻ, of the number of accidents per day is not equal to 0.31. A random sample of 17 recent days had a mean of 2 accidents per day with a variance of 0.62. If we assume that the number of accidents per day is approximately normally distributed, is there sufficient evidence to conclude, at the 0.05 level of significance, that the actuaries are correct? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO O20 (c) Find the value of the test statistic. (Round…
- 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…Please use ANOVAA researcher wants to measure average cardiovascular health of university students and compare those scores to the average scores in the general population. Assuming that population variance is known, what statistical test is most appropriate for this study? independent-samples t-test single-sample t-test z-test for sample mean related-samples t-test
- A professor claims that the final exam grades are more widely dispersed in Principles classes compared to upper-level classes. In a sample of 101 Principles final exams, the standard deviation is 16 while in a sample of 30 upper-level class final exams the standard deviation is 13. Test the hypothesis at the 10% level of significance that the 2 variances are different. Write all formulas and hypothesis.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…
