7. [Multiple Choices}(d)of rhesus monkeys that live in a captive breeding facility and were assigned to research studies is (0.67,0.83). Which of the following is true?Based on a random sample of 120 rhesus monkeys, a 95% confidence interval for the proportionCircle only ONE correct answer in each question. No explanations needed.(a)Which of the following is true regarding the Central Limit Theorem (CLT)?(i) 95 of the sampled monkeys were assigned to research studies(i) If your sample size is n = 30 exactly, then you are guaranteed to have an approximately normalsampling distribution of the sample mean.(ii) the margin of error for the confidence interval is 0.16(iii) a larger sample size would yield a wider confidence interval(ii) As the sample size n increases, the data distribution should become approximately normal.(iv) none of the above are true(iii) The Central Limit Theorem states that the sampling distribution of the sample mean should alwayshave the same shape as the population distribution.(e)evaluate the test results to determine if there is enough evidence toComplete the following sentence: When conducting a hypothesis test, weand then(iv) none of the above(i) Assume that the null hypothesis is false; accept the null hypothesis(b)sample of 10 teenage girls, would the sampling distribution of average BMI follow an approximately normalSuppose the population distribution of BMI among teenage girls is right-skewed. If you took a(ii) Assume that the null hypothesis is true; reject the null hypothesisdistribution?(iii) Assume that the alternative hypothesis is true; reject the null hypothesis(i) Yes, because the shape of the population distribution does not affect the shape of the sampling(iv) Assume the alternative hypothesis is false; reject the alternative hypothesisdistribution(ii) No, because the underlying population distribution is right-skewed, so no matter the sample size thesampling distribution cannot be normal.(iii) Yes, because we have more than ten observations, and according to the Central Limit Theorem thatis large enough for the sampling distribution to be close to bell-shaped even though the underlyingpopulation distribution is right-skewed(f)of the following would be plausible 95% confidence interval for u?Suppose a t-test yields a p-value of 0.02 when testing hypotheses Ho: µ = 0 vs Ha: µ 0. Which(i) (1.3, 3.4)(ii) (-3.4, 1.3)(iї) (-1.3, 3.4)(iv) No, because the underlying population distribution is right-skewed and we have less than 30 obser-vations, which is the cutoff used for the Central Limit Theorem to apply.(iv) (-3.4, -1.3)(c)birth weight of rhesus monkeys born in captivity. Below are the summary statistics of the data and outputfrom the analysis testing if the true average birth weight of the monkeys is 0.4kg. What is the correctcalculation to estimate the true average birth weight of rhesus monkeys with a 95% confidence interval?Veterinarians at a nonhuman primate research center are interested in estimating the true average(g)linear regression to explore the relationship between the number of calories and amount of carbohydrates(in grams) Starbucks food menu items contain. The estimated regression equation with carbohydratesas the response variable and the calories as the explanatory variable is ŷstatistics of the two variables is provided below.Seventy-six Starbucks food items were analyzed for the calorie and carbohydrate content. We used= 8.94 + 0.11x, and summaryminQ1 medianQ3max meansdn missing0.27 0.370.39 0.5 0.68 0.44 0.12 10variable minQ1 median Q3sdn missingmaxmeancalories80 300350 420500338.8105.4 779, p-value = 0.306alternative hypothesis: true mean is not equal to 0.4t = 1.0853, df =carbohydrates163145 598044.916.6 7795 percent confidence interval:ХXXXXXX XXXXWhich of the following is a true statement regarding the slope?(i) There is a positive association between calorie and carbohydrate content; however, because the slope(=0.11) is small, the association between calories and carbohydrates is weak.(i) 0.44 + 1.0853 × 0.12/V9(ii) 0.44 ±1.0853 × 0.12(ii) A food item that has 100 calories above average is expected to have 11 more gram carbohydratesover the average carbohydrates in the data.(iii) 0.44± 2.26 × 0.12//10(iv) 0.39 ± 1.96 × 0.12(iii) Because a the lowest calorie content of food observed is 80, and the slope 0.11 is well below thislowest value, this is extrapolation and cannot be trusted.(iv) All statements are true.

Question

7. [Multiple Choices}(d)of rhesus monkeys that live in a captive breeding facility and were assigned to research studies is (0.67,0.83). Which of the following is true?Based on a random sample of 120 rhesus monkeys, a 95% confidence interval for the proportionCircle only ONE correct answer in each question. No explanations needed.(a)Which of the following is true regarding the Central Limit Theorem (CLT)?(i) 95 of the sampled monkeys were assigned to research studies(i) If your sample size is n = 30 exactly, then you are guaranteed to have an approximately normalsampling distribution of the sample mean.(ii) the margin of error for the confidence interval is 0.16(iii) a larger sample size would yield a wider confidence interval(ii) As the sample size n increases, the data distribution should become approximately normal.(iv) none of the above are true(iii) The Central Limit Theorem states that the sampling distribution of the sample mean should alwayshave the same shape as the population distribution.(e)evaluate the test results to determine if there is enough evidence toComplete the following sentence: When conducting a hypothesis test, weand then(iv) none of the above(i) Assume that the null hypothesis is false; accept the null hypothesis(b)sample of 10 teenage girls, would the sampling distribution of average BMI follow an approximately normalSuppose the population distribution of BMI among teenage girls is right-skewed. If you took a(ii) Assume that the null hypothesis is true; reject the null hypothesisdistribution?(iii) Assume that the alternative hypothesis is true; reject the null hypothesis(i) Yes, because the shape of the population distribution does not affect the shape of the sampling(iv) Assume the alternative hypothesis is false; reject the alternative hypothesisdistribution(ii) No, because the underlying population distribution is right-skewed, so no matter the sample size thesampling distribution cannot be normal.(iii) Yes, because we have more than ten observations, and according to the Central Limit Theorem thatis large enough for the sampling distribution to be close to bell-shaped even though the underlyingpopulation distribution is right-skewed(f)of the following would be plausible 95% confidence interval for u?Suppose a t-test yields a p-value of 0.02 when testing hypotheses Ho: µ = 0 vs Ha: µ > 0. Which(i) (1.3, 3.4)(ii) (-3.4, 1.3)(iї) (-1.3, 3.4)(iv) No, because the underlying population distribution is right-skewed and we have less than 30 obser-vations, which is the cutoff used for the Central Limit Theorem to apply.(iv) (-3.4, -1.3)(c)birth weight of rhesus monkeys born in captivity. Below are the summary statistics of the data and outputfrom the analysis testing if the true average birth weight of the monkeys is 0.4kg. What is the correctcalculation to estimate the true average birth weight of rhesus monkeys with a 95% confidence interval?Veterinarians at a nonhuman primate research center are interested in estimating the true average(g)linear regression to explore the relationship between the number of calories and amount of carbohydrates(in grams) Starbucks food menu items contain. The estimated regression equation with carbohydratesas the response variable and the calories as the explanatory variable is ŷstatistics of the two variables is provided below.Seventy-six Starbucks food items were analyzed for the calorie and carbohydrate content. We used= 8.94 + 0.11x, and summaryminQ1 medianQ3max meansdn missing0.27 0.370.39 0.5 0.68 0.44 0.12 10variable minQ1 median Q3sdn missingmaxmeancalories80 300350 420500338.8105.4 779, p-value = 0.306alternative hypothesis: true mean is not equal to 0.4t = 1.0853, df =carbohydrates163145 598044.916.6 7795 percent confidence interval:ХXXXXXX XXXXWhich of the following is a true statement regarding the slope?(i) There is a positive association between calorie and carbohydrate content; however, because the slope(=0.11) is small, the association between calories and carbohydrates is weak.(i) 0.44 + 1.0853 × 0.12/V9(ii) 0.44 ±1.0853 × 0.12(ii) A food item that has 100 calories above average is expected to have 11 more gram carbohydratesover the average carbohydrates in the data.(iii) 0.44± 2.26 × 0.12//10(iv) 0.39 ± 1.96 × 0.12(iii) Because a the lowest calorie content of food observed is 80, and the slope 0.11 is well below thislowest value, this is extrapolation and cannot be trusted.(iv) All statements are true.

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