In a t distribution, the critical values will always be the same (not dependent on sample size).TrueFalse
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- Assume the samples are random and independent, the populations are nomally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At a = 0.10, is there enough evidence conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below. E Click the icon to view the battery cost data. (a) Let u1. P2. H3 represent the mean prices for the group size 35, 65, and 24/24F respectively. Identify the claim and state Ho and H. H Cost of batteries by type The claim is the V hypothesis. Group size 35 Group size 65 Group size 24/24F 101 111 121 124 D 146 173 182 278 124 140 141 89 (b) Find the critical value, Fo, and identify the rejection region. 90 79 84 The rejection region is F Fo, where Fo = (Round to two decimal places as needed.) (c) Find the test statistic F. Print Done F= (Round to two decimal places as…A professor wants to know whether or not there is a difference in comprehension of a lab assignment among students depending on if the instructions are given all in text, or if they are given primarily with visual illustrations. She randomly divides her class into two groups of 15, gives one group instructions in text and the second group instructions with visual illustrations. The following data summarizes the scores the students received on a test given after the lab. Let the populations be normally distributed with a population standard deviation of 5.32 points for both the text and visual illustrations. Text (Group 1) Visual Illustrations (Group 2) 57.3 59 45.3 57.6 87.1 72.9 61.2 83.2 43.1 64 87.3 76.7 75.2 78.2 88.2 64.4 67.5 89 86.2 72.9 67.2 88.2 54.4 43.8 93 97.1 89.2 95.1 52 84.1 Is there evidence to suggest that a difference exists in the comprehension of the lab based on the…Explain how to find the critical values for a t-distribution. Click the icon to view the t-distribution table. Give the first step. Choose the correct answer below. O A. Identify the level of significance and the degrees of freedom, d.f. =n-1. 2 O B. Identify the level of significance 1- a and the degrees of freedom, d.f. = n. c. Identify the level of significance a and the degrees of freedom, d.f. = n-1. 1-a O D. Identify the level of significance and the degrees of freedom, d.f. = n. 2 Find the critical value(s) using the given t-distribution table in the row with the.correct degrees of freedom. column with a V sign. If the hypothesis test is left-tailed, use the "One tail, a" "Two tails, "Two tails, a" "One tail, 5
- A researcher wants to know if there is a difference between the mean amount of sleep that people get for various types of employment status. The table below shows data that was collected from a survey. Full Time Worker Part Time Worker Unemployed 6 6 7 5 6 7 8 9 9 7 6 8 8 8 8 8 8 8 6 6 8 8 7 6 9 Assume that all distributions are normal, the three population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of α=0.01α=0.01.H0: μ1=μ2=μ3H0: μ1=μ2=μ3H1:H1: At least two of the means differ from each other. For this study, we should use Select an answer 2-PropZTest 2-PropZInt 1-PropZInt 2-SampTInt 1-PropZTest T-Test χ²-Test ANOVA χ²GOF-Test TInterval 2-SampTTest The test-statistic for this data = (Please show your answer to 3 decimal places.) The p-value for this sample = (Please show your answer to 4 decimal places.) The p-value is Select an answer less than (or equal to) alpha greater…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…If a distribution of data follows a normal distribution, we would expect that the __________, and __________ are all equal.
- In this exercise involving paired differences, consider that it is reasonable to assume the populations being compared have approximately the same shape and that the distribution of paired differences is approximately symmetric. Percents of on-time arrivals for flights in 2006 and 2007 were collected for 11 randomly selected airports. Suppose data for these airports follow. Airport 1 2 3 4 5 6 7 9 10 11 Percent On-Time 2006 71.78 68.23 78.98 78.71 78.59 76.67 What is your conclusion? 77.67 75.29 70.39 79.91 74.55 2007 68.69 65.88 79.40 Find the value of the test statistic. T = 63 ✓ 75.78 73.45 78.68 75.38 71.98 62.84 76.49 Use a = 0.05 to test the hypothesis that there is no difference between the median percent of on-time arrivals for the two years. State the null and alternative hypotheses. 72.42 O Ho: Median percent on-time in 2006 - Median percent on-time in 2007 = 0 H₂: Median percent on-time in 2006 - Median percent on-time in 2007 + 0 O Ho: Median percent on-time in 2006 -…Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Assume that the distributions for each state are normal and that all variances are equal. Arkansas 4.8 4.9 5.0 5.4 5.4 5.4 5.6 5.6 5.6 5.9 6.0 6.1 California. 1.5 3.7 4.0 4.5 4.9 5.1 5.3 5.4 5.4 5.5 5.6 5.6 Texas. 5.6 5.8 6.6 6.9. 6.9 6.9 7.1 7.3 7.5 7.6 7.7 7.7A 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…