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Question 1 Choose the most appropriate conclusion drawn from the Excel output below that tests for a difference i n the weights of male and female babies: tT- est: Two-Sample Assuming Equal Variances males females Mean 3.386 3.073 Variance 0.11S6 0.2190 Observations 10 10 Pooled Variance 0.4090 Hypothesized Mean 0 Difference df 18 t Stat 1.71 P{T <=t) one-tail 0.0S2 t Critical one-tail 1.7341 P{T <::::t) two-tail 0.105 t Critical two-tail 2.1009 Select one: 0 a. There is a significant difference in babies mean weights, females weigh more on average than males. 0 b. There is no significant difference in babies mean weights. The mean weights could be the same for males and females. 0 c. None of the other options 0 d. There is a significant difference in babies mean weights, males weigh more on average than females. Question 2 Question 3 A health and wellbeing committee claims that working an average of 38 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 approproate hypothesis test to answer the following research question: Are full-time employees working an average of 38 hours per week? Weekly working hours 50 41 41 34 39 45 31 27 29 24 34 29 28 34 33 1. (1 mark) The most appropriate hypothesis test for these data is: Pick One A one-sample t-test where sigma is known A one-sample t-test where sigma is unknown A two-sample t-test A paired t-test None of the other options 2. (1 mark) The null hypothesis is that the mean working hours per week is equal to 38 or 34.6? 3. (1 mark) What the value of the test statistic? Round your answer to 3dp. 4. (1 mark) What is the p-value for this test statistic? Round your answer to 3dp. 5. (1 mark) What is the most appropriate conclusion for this test? There no evidence against the null hypothesis, the mean working hours could be as claimed by the committee There is evidence against the null hypothesis, the mean working hours are significantly less than those claimed by the committee There is evidence against the null hypothesis, the mean working hours are significantly more than those claimed by the committee 30 25 20 10 I I Scatterplot of PCB vs Age : . i . 6 10 Histogram (response is PCS) 18 16 14 12 r JO t 12 ·8 .. 4 f:l(l:Skluat Versus Fits (re.sl>OOse IS PCB) 20 15 10 . ! 5 . - . . . . ·5 . ·10 12 16 • 10 12 " ,. 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: 0 a. No, the residuals are not evenly spread either side of the horizontal line for the range of x-values 0 b. None of the assumptions appear to be satisfied. 0 c. No, the histogram of the residuals is not sufficiently symmetric 0 d. Yes 0 e. No, the relation does not look linear 18 Question 4 Question 5 Question 6 A study was undertaken to compare two soft drinks. Each drink was rated on a numerical scale of Oto 100, with 100 being the highest rating. Each of 17 subjects tried both drinks with a coin tossed to determine which drink would be tried first. The drinks were the same colour and were served in clear plastic cups. t-Test Paired Two Sample for Means Drink A Drink B Mean 70.35 69.29 Variance 161.37 172.72 Observations 17 17 Pearson Correlation 0.918 Hypothesized Mean Difference 0 df 16 t Stat 0.8335 P(T <=t) one-tail 0.2084 t Critical one-tail 1.7459 P(T <=t) two-tail 0.4168 t Critical two-tail 2.1199 Consider the Excel output above and answer the following questions: 1. Does there appear to be a difference between drink preference ratings, on average? {Y} Yes or {N} No 2. What is the absolute value of the t statistic? (2 dp} 3. What are the degrees of freedom? (integer) 4. What is the p-value? (2 dp} 5. Do you reject or not reject the null hypothesis? (A} Reject or (B} Not reject You want to compare the daily sales for two different designs of Web pages for your Internet business. You assign 30 days to design A and 30 days to design B and record sales each of these days. What type of a test would you use for this comparison? Select one: 0 a. A two-sample t-test. 0 b. A paired t-test. A study of working conditions in a city recorded the time and distance that people in various cities spend travelling to work each day. The following output was obtained from a sample of 25 people who work: n mean standard deviation Time (minutes) 25 42.55 12.65 Distance (km) 25 16.65 4.95 Assuming travel times are known to follow a normal distribution, calculate a 95% confidence interval to estimate the average travel time for all people who worked. Select one: 0 a. (40.02, 45.08) 0 b. none of these options 0 c. (37.59, 47.51) 0 d. (42.49, 42.61) 0 e. (37.33, 47.77) Question 7 Question 8 Question 9 Consider a large clothing shop. Suppose it is known that the number of business suits sold per day is normally distributed with a mean, I.I = 21 and standard deviation, a = 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 between 16 and 26 business suits? {4 dp) Predicting resting pulse rate: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations Intercept Height 0.1845 0.0340 0.0223 10.6861 84 Coefficients 110.8092 -0.5479 Standard Error 22.2463 0.3223 t Stat 4.9810 ..... P-value 0.0000 0.0930 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 bo? {1 dp) 2. What is the value of b1? {4 dp) 3. What is the se(b1)? {4dp) 4. Calculate the absolute value of the test statistic for b1. (2dp) 5. What is the goodness of fit (as a percentage)? {1 dp) 6. What is the correlation? {2 dp) 7. Would you (A) reject or (B) not reject the hypothesis that 􀁦1 =0? The coefficient of determination, R2, tells us: Select one: 0 a. All of the other answers. 0 b. How to describe a relationship. 0 c. The proportion of variability in y accounted for by x. 0 d. How to determine someone's score.

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Q1 (b)
Q2 1. One sample t test where sigma is unknown
2. equal to 38...

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