Multiple Choice Monday #2 23-24

For a middle school science project, Jalen measured the pH of 25 vinegar products. The summary statistics for the values of the pH are shown in the following computer output. Based on the 1.5 x IQR rule for outliers, which of the following statements is true?

• A) The minimum pH value of 2.11 is an outlier, and no other pH value could be identified as an outlier.

• B) The maximum pH value of 2.93 is an outlier, and no other pH value could be identified as an outlier.

• C) The minimum pH value of 2.11 is an outlier, and there could be other pH values identified as outliers that are below the first quartile, but no pH value above the third quartile could be identified as an outlier.

• D) The maximum pH value of 2.93 is an outlier, and there could be other pH values identified as outliers that are above the third quartile, but no pH value below the first quartile could be identified as an outlier.

• E) There are no pH values that could be identified as outliers.

The tail length of Siberian tigers is approximately normally distributed with a mean of 0.85 meter and a standard deviation of 0.13 meter. Which of the following is the best interpretation of the z-score for a particular Siberian tiger with a tail length of 0.8 meter?

• A) The tiger’s tail length is approximately 0.38 standard deviation below the mean.

• B) The tiger’s tail length is approximately 0.38 standard deviation above the mean.

• C) The tiger has an approximate 0.38 probability of having a tail length of 0.8 meter.

• D) The tiger’s tail length is approximately 0.0065 meter greater than the standard deviation.

• E) The tiger’s tail length is approximately 0.05 meter below the mean.

Tags

CCSS.HSS.ID.A.4

Suppose a hypothesis test will be used to investigate whether the proportion of United States adults who have been a victim of a cybercrime, such as identity theft, is greater than 0.25. Suppose that the hypothesis test is conducted using a significance level of 0.05 and the power of the test is determined for a specific alternative value using the significance level of 0.05. If the significance level of the hypothesis test is changed to 0.01 and the power of the test is computed for the same alternative value using a significance level of 0.01, which of the following best describes the change(s) to the probability of a Type I error and the power of the test?

• A. The probability of a Type I Error would decrease, and the power of the test would stay the same.

• B. The probability of a Type I Error would decrease, and the power of the test would increase.

• C. The probability of a Type I Error would decrease, and the power of the test would decrease.

• D. The probability of a Type I Error would increase, and the power of the test would increase.

• E. The probability of a Type I Error would increase, and the power of the test would decrease.

An agriculturalist wants to estimate the average time from germination to ripe fruit for a new type of seedless strawberry. From a random sample of 25 seedless strawberries of the new type, the mean time from germination to ripe fruit is 42.1 days with standard deviation 3.6 days. Assume all conditions for inference were met. Which of the following is a 90 percent confidence interval for the mean time from germination to ripe fruit for the new type of seedless strawberry?

• A. 42 ± 6.16

• B. 42.1 ± 1.49

• C. 42.1 ± 1.23

• D. 42.1 ± 1.18

• E. 42.1 ± 0.25

Tags

CCSS.HSS.IC.B.4

A large company has operated assuming that the rate of absenteeism is the same for each day of the week. The new human resources director at the company claims that the assumption is false and that the rate of absenteeism is different for some days of the week as compared with others. To test the claim, a random sample of 150 absences was selected, and the day of the week on which the absence occurred was recorded. The counts are shown in the following table. The appropriate chi-square test will be performed to test the claim. What is the contribution of the Monday absences to the calculation of the chi-square test statistic?

• A. 0.333

• B. 2.500

• C. 3.000

• D. 3.333

• E. 10.000

1. A large online retailer places packed and ready-to-be-shipped boxes in a line on a conveyor belt. A sample of boxes will be used to estimate the mean weight of boxes shipped on a given day. One proposed method for selecting the sample is as follows:

   1. 1. Generate a random integer from 1 to 20.
      2. Use that integer to select an initial box from the first 20 boxes in line on the conveyor belt.
      3. Select every 25th box that follows the initial box on the conveyor belt for the rest of the day.

   Which of the following best describes the proposed sampling method?

• 0. Stratified random sample, stratified by time of day

• 0. Cluster sample, with times of day as clusters
     

• 0. Cluster sample, with box weights as clusters
     

• 0. Systematic random sample

• 0. Convenience sample

Tags

CCSS.HSS.IC.B.3

1. An experiment was conducted to investigate whether submersion in cold water causes a lower heart rate. The experiment used 50 volunteers. The 25 youngest volunteers had their heart rate measured while holding their breath for 30 seconds with their face submerged in cold water. The 25 oldest volunteers had their heart rate measured while holding their breath for 30 seconds with their face not submerged in cold water. The mean heart rate for volunteers who had their face submerged in cold water was lower than the mean heart rate for volunteers who did not have their face submerged in cold water.

   Which of the following elements of a well-designed experiment is missing?

2. I. Comparison of at least two treatment groups

   II. Random assignment of treatments to experimental units

3. III. Replication

• I only

• II only

• I and II only

• II and III only

• I, II, and III

Tags

CCSS.HSS.IC.B.3

The probability that a particular electrical component operates successfully is 3/4 . An electrical system consists of three such components that operate independently. The system will function successfully if at least one of the three components operates successfully.
What is the probability that the system will function successfully?

• 1/64

• 27/64

• 37/64

• 3/4

• 63/64

The driving route between a student’s home and the student’s high school has two traffic lights. The distribution of total time spent driving has mean 5 minutes and standard deviation 1 minute. The distribution of time spent waiting at a light has mean 0.75 minute and standard deviation 0.25 minute. The total time spent driving and the time spent waiting at a light are independent. The total travel time from the student’s home to the student’s high school consists of the total time spent driving and the time spent waiting at two lights.

What are the mean and the standard deviation of the total travel time?

• The mean is 5.75 minutes and the standard deviation is about 1.03 minutes.

• The mean is 5.75 minutes and the standard deviation is about 1.06 minutes.

• The mean is 6.5 minutes and the standard deviation is about 1.06 minutes.

• The mean is 6.5 minutes and the standard deviation is about 1.12 minutes.

• The mean is 6.5 minutes and the standard deviation is about 1.5 minutes.

A national newspaper reported that 40 percent of high school students engage in community service activities. A school administrator wondered whether the proportion of high school students at the administrator’s school who engage in community service activities is less than 40 percent. The administrator selected a random sample of 100 students, and 36 responded that they do engage in community service activities. The conditions for inference were met, and an appropriate hypothesis test resulted in a p-value of 0.207.

Which of the following is a correct interpretation of this p-value?

• 1. The probability that a randomly selected student at this high school engages in community service

     activities is 0.207.

• 1. The probability is 0.40 that less than 20.7 percent of students at this high school engage in community service activities.

• 1. The probability is 0.207 that less than 40 percent of students at this high school engage in community service activities.

• 4. If the proportion of all students at the school who engage in community service activities is 0.4, the probability of observing 36 or fewer in a random sample of 100 students who engage in community service activities is 0.207.

• 4. If the proportion of all students at the school who engage in community service activities is 0.36, the probability of obtaining 40 or fewer in a random sample of 100 who engage in community service activities is 0.207.