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Question 1 Scatterplot of Weight vs Length Histogram Versus Fits [response is Weight) (response is Weight) 500 - 30 - 200 400 . 25. 150 20 - 100 300 Frequency 15 Residual 200 - 10 100 -50 -100 40 50 6 70 80 -80 -40 40 80 120 150 100 200 300 400 Length Residual Fitted Value For the plots above regarding a regression of the carcinogen PCB (polychlorinated biphenyl) versus age in a sample of trout, are all the assumptions met? Interpret residuals versus fits as you would residuals versus x. Select the best answer. Select one: a. None of the assumptions appear to be satisfied. b. No, the relation does not look linear c. No, the residuals are not evenly spread either side of the horizontal line for the range of x-values d. Yes e. No, the histogram of the residuals is not sufficiently symmetrichuestion 2 Predicting resting pulse rate: Regression Statistics Multiple R 0.0778 R Square 0.0060 Adjusted R Square -0.0061 Standard Error 15.9189 Observations 84 Coefficients Standard Error t Stat P-value Intercept 103.0496 33.1397 3.1095 0.0026 Height -0.3389 0.4802 **** 0.6163 The Excel output above is from a regression of the resting pulse rate on height. Use the output to answer the following questions. 1. What is the value of be? (1 am=Answer 2. What is the value of hi? (4 gm=Answer 3. What is the se(b1)? (4gg=Answer 4. Calculate the absolute value of the test statistic for {31. (zgg)=Answer 5. What is the goodness of t (as a percentage)? (1 am=Answer 6. What is the correlation? (2 Whenever 7. Would you (A) reject or (B) not reject the hypothesis that 81:0? Answer Question 3 Consider a large clothing shop in Sydney. Suppose it is known that the number of business suits sold per day is normally distributed with a mean, u = 20 and standard deviation, 0 = 10. Mr Wood is employed to sell business suits. The number of business suits he sells each day for 30 days is recorded and the mean number per day calculated. What is the probability that Mr Wood's average daily sales will be more than 26 business suits? (4 dm=Answer Question 4 A population is normally distributed with a known standard deviation, o = 10 units. A random sample of size 64 is obtained from this population. The mean of this sample is 40. 1. What is the lower limit of the 95% confidence interval for the population mean ? (1 do) Answer 2. What is the upper limit of the 95% confidence interval for the population mean ? (1 do) AnswerQuestion 5 A health and wellbeing committee claims that working an average of 37 hours per week is recommended for maintaining a good work-life balance. A random sample of 15 full-time employees were surveyed about how many hours they worked; the data are shown below. You may assume that the data come from a population that is normally distributed. Use Excel and an Whypothesis test to answer the following research question: Are full-time employees working an average of 37 hours per week? Weekly working hours 40 53 32 47 41 1. 34 32 52 50 48 41 19 52 35 30 (1 mark) The most appropriate hypothesis test for these data is: W one- sample t-test where sigma is m one-sample t-test where sigma is WMo-sample t-tgm paired pm of the other options (1 mark) The null hypothesis is that the mean working hours per week is equal to Answer3740.4. (1 mark) What the value of the test statistic? Round your answer to 3dp. Answer (1 mark) What is the p-value for this test statistic? Round your answer to 3dp. Answer (1 mark) What is the most appropriate conclusion for this test? MKS-51.13% no evidence against the null hypothesis, the mean working hours could be as claimed by the W is evidence against the null hypothesis, the mean working hours are significantly less than those claimed by the Wis evidence against the null hypothesis, the mean working hours are significantly more than those claimed by the committee Question 6 Below are the results of a study that compared blood pressure measurements while standing with blood pressure measurements while supine (lying down) in 12 subjects. Each of these 12 subjects had their blood pressure measured in both positions. You may assume that the differences are normally distributed. t-Test: Paired Two Sample for Means standing supine Mean 138.36 137.50 Variance 164.81 164.93 Observations 12 12 Pearson Correlation 0.994 Hypothesized Mean Difference O df 11 t Stat 2.0752 P(T