The hypotheses for this test are: 0 H03 \"automatic = \"manual H33 \"automatic : \"manual 0 H03 \"automatic = \"manual H33 \"automatic > \"manual 0 H03 \"automatic = \"manual H33 \"automatic 0/1 pt 9 3 99 0 Details 5.32 Fuel efficiency of manual and automatic cars, Part 1: Each year the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions manufactured in 2012. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? Assume that conditions for inference are satisfied. City MPG, Automatic City MPG, Manual Mean 16.12 19.85 SD 3.58 4.51 n 26 26 35 25 HH IH 15 automatic manual City MPG0 Question 11 v Ed on pt '0 3 8 99 G) Details You are conducting a study to determine if there is a signicant difference between typical salaries of surgeons and stock brokers (in thousands of dollars). Calculate the test- statistic, t with the following sample data. n1: 20,i1: 142, 31 : 3 n2 : 25, i2 : 139, 32 = 3 Rounded to 2 decimal places. Question 7 a 0m pts '0 3 8 99 (D Details You wish to test the following claim (Ha) at a signicance level of a : 0.01. For the context of this problem, pd : p2 M where the first data set represents a pre- test and the second data set represents a posttest. Hozpd I 0 Haipd > 0' You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pretest and post-test samples for n_: 20 subjects. The average difference (post - pro) is d : 44.9 with a standard deviation of the differences of 30; : 46.7. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = l ' What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =' l The p-value is... 0 less than (or equal to) o: O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null (d) What type of error might we have made? Explain what the error means in the context of the application. 0 Throwing Error 0 Fielding Error 0 Type | 0 Type H (e) Based on the results of this hypothesis test, would you expect a condence interval for the average difference between the reading and writing scores to include 0? Explain your reasoning. 0 yes, because there is almost a 0% chance that average reading and writing scores are the same 0 no, because we rejected the idea that average reading and writing scores are equal 0 no, because most people will not earn an average score of 0 on either exam 0 yes, because the evidence was not strong enough to suggest that average reading and writing scores differ (b) Create hypotheses appropriate for the following research question: is there an evident difference in the average scores of students in the reading and writing exam? 0 H0: \"diff = 0 Ha: l-ldiff 0 0 H01 IJdiff = 0 Ha: leiff it 0 (c) The average observed difference in scores is Miread _ write = {1.545, and the standard deviation of the differences is 8.887 points. Do these data provide convincing evidence of a difference between the average scores on the two exams? The test statistic is: l ' (please round to twodecimal places) The pvalue is: ' '(please round to four decimal places) The conclusion of the test is: 0 Since p IL/ on pt '0 3 8 99 G) Details A survey of 41 people was conducted to compare their selfreported height to their actual height. The difference between reported height and actual height was calculated. You're testing the claim that the mean difference is greater than 1.5. From the sample, the mean difference was 1.85, with a standard deviation of 0.5. Calculate the test statistic, rounded to two decimal places :l