Unit Test — Unit test Answers

A statistics teacher has 20 students in her class. Here is a graph showing the scores of the 20 students on a recent test.The teacher selects a random sample of 5 students from the class. Here is a graph displaying the scores of the students she selected.The teacher calculates the mean of this sample of 5 scores and plots it on a number line. She then repeats this process 100 times. Here are the results.

The proportion of all high school students who watch national news is p = 0.57. A random sample of 60 high school students is selected. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

The number of pieces of dog food in a one-cup scoop is approximately Normally distributed with a mean of 205 pieces and a standard deviation of 9.2 pieces. If a random sample of 15 scoops of dog food is selected, what is the probability that the mean number of pieces of food will be less than 200 pieces?

The governor of Florida would like to estimate the mean age of all Florida residents. To do so, he randomly selects 500 Florida residents and determines their mean age to be 58.2 years. However, according the most recent census data, the mean age of all Florida residents is 55.6 years. Which of the following properly describes the number 58.2?

The number of turns of a pencil sharpener needed to sharpen a brand W pencil is approximately Normally distributed with a mean of 4.6 and a standard deviation of 0.67. The number of turns needed to sharpen a brand H pencil is approximately Normally distributed with a mean of 5.2 and a standard deviation of 0.33. If 30 pencils of each brand are randomly selected and sharpened, what is the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H?

A spinner with four equal sectors labeled "purple,” "blue,” "orange,” and "green” is spun 45 times. What is the probability that the spinner will land on "purple” in fewer than 20% of the spins?Find the z-table here.

A real estate agent in a large city claims to sell 15% of their houses within two months of the original listing. A random sample of 75 listings is chosen, and 9 were sold within two months of the original listing. Let = the proportion of houses in the random sample that were sold within two months.The probability of 12% or fewer of this real estate agent’s listings being sold within two months is 0.295. Does this result provide convincing evidence against the agent’s claim?

A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p = the true proportion of times the dime would land on heads when spun. Under the assumption that the true proportion is 0.5, 100 simulated proportions for samples of size 25 are shown in the dotplot. Using the dotplot, what do the two dots above 0.70 represent?

The proportion of all high school students who watch national news is p = 0.47. A random sample of 50 high school students is selected. Which of the following is the mean of the sampling distribution of ?

The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. A baseball analyst randomly selects 40 athletes and records the mean salary. What is the shape of the distribution of the sample mean for all possible random samples of size 40 from this population?

Alex’s times for running a mile are Normally distributed with a mean time of 5.28 minutes and a standard deviation of 0.38 seconds. Chris’s times for running a mile are Normally distributed with a mean time of 5.45 seconds and a standard deviation of 0.2 seconds. Ten of Alex’s times and 15 of Chris’s times are randomly selected. Let represent the difference in the mean times for Alex and Chris. Which of the following represents the standard deviation of the sampling distribution for ?

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The proportion of officers who are younger than 18 is 0.6. The table displays all possible samples of size 2 and the corresponding proportion for each sample.Using the proportions in the table, is the sample proportion an unbiased estimator?

The distribution of tips given by customers who buy one cup of coffee is bimodal with a mean of $0.29 and a standard deviation of $0.1164. If a random sample of 50 tips from customers who buy one cup of coffee is selected, is it appropriate to calculate the probability of a sample mean being more than $0.32 using an approximately Normal model?

Among the senior class at a high school, 55% of Ms. Keating’s students plan on majoring in a branch of STEM, while 49% of Ms. Lewis’s students plan on majoring in a branch of STEM. Suppose Ms. Keating chooses 25 of her students at random and Ms. Lewis chooses 23 of her students at random. Since nKpK, nK (1 – pK) and nLpL, nL (1 – pL) are all greater than 10, the Normal condition is met. Let K = the proportion of Ms. Keating’s students from the sample who plan on majoring in a branch of STEM, and let L = the proportion of Ms. Lewis’s students from the sample who plan on majoring in a branch of STEM. What is the probability that the proportion of students who plan on majoring in a branch of STEM is greater for Ms. Keating?Find the z-table here.

In bags of Happy Trail Mix, the number of raisins is skewed left with a mean of 33.6 and a standard deviation of 8.4, while in bags of a generic trail mix, the number of raisins is skewed right with a mean of 28.8 and a standard deviation of 12.7. What is the probability in a sample of 17 randomly selected Happy Trail Mix bags and a sample of 17 randomly selected generic bags that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix?

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let and be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class.Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions.Session A: $50Session B: $50Session C: $100Session D: $150Session E: $200

At a local veterinary office, 48% of dogs get their teeth cleaned, while 35% of cats get their teeth cleaned. Let and be the sample proportions of dogs and cats at this veterinary office, respectively, who get their teeth cleaned. Suppose 25 dogs and 32 cats from this veterinary office are selected at random to collect data on their teeth-cleaning history.Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

The owner of a tire company wants to determine how long a new type of tire tread will last by measuring the length of time, in days, it takes for the tire tread to reach 2 mm. Let μ = the true mean number of days it takes for the tire tread to wear to 2 mm. Which of the following sample sizes will have the least variability in the sampling distribution of the sample mean?

In an urban area, 31% of dog owners pay for someone to walk their dogs. Morgan asks a random sample of 50 dog owners in this urban area if they pay for someone to walk their dog. What is the probability that more than 30% of the owners in the sample pay for someone to walk their dog?Find the z-table here.