Question 1 1 pts At a large university, the on-campus housing services surveyed a random sample of 45 rst-year students and 58 second-year students from populations of over 1,000 rst-year students and 1,000 second-year students. The sampled students were asked how many hours they spend per week using the kitchens in their dorms. Let $1 represent the average hours per week spent in the kitchen by the 45 rst-year students, and let :52 represent the average hours per week spent in the kitchen by the 58 second-year students. Which of the following is the best explanation for why the sampling distribution of 5:1 5:2 can be modeled with a normal distribution? 0 The two standard deviations are assumed to be equal. 0 The distributions of the populations are normal. 0 The sample sizes are both sufciently large. 0 There are at least 30 students in each of the two populations. Question 2 1 pts Suppose the standard deviation of the height of a pine tree in the Jefferson National Forest is 10 ft and the standard deviation of the height of an oak tree in the Jefferson National Forest is 3 ft. Let :Ep represent the average height of ve randomly selected pine trees in the Jefferson National Forest and let 5:0 represent the average height of six randomly selected oak trees from the Jefferson National Forest. If the random sampling is done without replacement, what is the standard deviation of the sampling distribution crip_jo of the sampling distribution of the difference in sample means Question 3 1 pts Two student clubs at a high school participated in many fundraisers throughout the school year. During a certain fundraiser, 160 people donated to club A with an average donation of if} = $9.50 and 120 people donated to club B with an average donation of $3 = $11.25. What is the correct unit of measure of the mean of the sampling distribution of EA 533? O Donations 0 Clubs 0 Dollars 0 People Question 4 1 pts The diameters of Red Delicious apples in a certain orchard are normally distributed with a mean [JR 2 2.54 inches and a standard deviation 0'}; = 0.32 inches. The diameters of Gala apples from another orchard are normally distributed with a mean pg 22.62 inches and a standard deviation of 0G = 0.41 inches. Suppose a random sample of size n=15 Red Delicious apples are selected and a random sample of size n=15 Gala apples are selected from these orchards. Which of the following best represents the mean and standard deviation of the sampling distribution of the difference in sample means :33 g? _ {0.32 0.41 N GERg F + F m; 0.219 0 \"Eric : 2.62 2.54 : 0.08 2 0.322 0.412 N OER5C! 15 'l 15 ~0.134 o Mrs-.6 = 2.54 2.62 = 0.08 {0.32 0.41 N OER5G = F + 15 N 0. 0 WHO : 2.54 2.62 : 0.08 _ 0.322 0.412 N Ugegc 15 -l- 15 ~0.134 Question 5 1 pts The diameters of Red Delicious apples in a certain orchard are normally distributed with a mean MR 2 2.54 inches and a standard deviation O'R : 0.32 inches. The diameters of Gala apples from another orchard are normally distributed with a mean pg 22.62 inches and a standard deviation of 0G = 0.41 inches. Suppose a random sample of size n=15 Red Delicious apples are selected and a random sample of size n=15 Gala apples are selected from these orchards. Determine and interpret P(:ER 7 Etc; 2 0) O P(:R :69 2 0)=0.2752 The probability that the diameters for all 15 Gala apples will exceed the diameters for all 15 Red Delicious apples is 0.2752. 0 P(:T:R 5G 2 0)=o.7248 Getting a difference (R-G) in sample mean diameters greater than or equal to 0 happens in about 72.48% of all possible samples of 15 Red Delicious apples and 15 Gala apples. This is not unusual. O P(:I:R g 2 0)=0.3145 The probability of observing a difference greater than or equal to 0 inches between the diameter of one Red Delicious apple and the diameter of one Gala apple is 0.3145. 0 P(a':R g 2 0)=0.2752 The probability of observing a difference (Red Delicious minus Gala) greater than or equal to 0 inches between the mean diameter of 15 Red Delicious apples and the mean diameter of Gala apples is 0.2752. This is not unusual