Question 1

In a clinical trial with 80 patients, 40 must be randomly selected for the intervention group. Which sampling method is most appropriate to ensure randomness?

Accepted Answer

Use a random number table to select 40 unique numbers from 1 to 80.

Question 2

Which of the following statements about a census is correct?

Accepted Answer

False, a census can include every student if all are counted.

Question 3

Which arithmetic operations are meaningful for ordinal data?

Accepted Answer

Ordering only; differences and ratios are not generally meaningful.

Question 4

Given the frequencies of 10, 20, and 30 for three categories, what is the total number of responses?

Accepted Answer

60

Question 5

A group of 25 people was surveyed about the number of cups of coffee they drink per day. The dot plot is shown. What is the most common number of cups, and how is the distribution shaped?

Accepted Answer

The most common number of cups is 2, and the plot is roughly symmetric around 2 cups per day.

Question 6

If a frequency polygon has class midpoints labeled as 20, 40, 60, and 80, what does a point at $$x=60$$ and $$y=20$$ represent?

Accepted Answer

The class with midpoint 60 has a frequency of 20.

Question 7

The boxplot shows the number of movies watched last month. What is the likelihood, as a percent, that a randomly selected person watched fewer than 2 movies last month?

Accepted Answer

About 25%

Question 8

A group of hikers recorded the distances they covered during a week: 7, 9, 11, 12, 14, 15, 17, 18, 20, 21. For the original data set and the 10% trimmed data set, which of the following is correct?

Accepted Answer

Mean: 14.4 (original), 14.5 (trimmed); Median: 14.5 (both); Mode: None (both); Midrange: 14 (original), 14.5 (trimmed)

Question 9

The following data set shows the weights (in kilograms) of 12 randomly selected backpacks: 7, 12, 9, 15, 20, 17, 11, 14, 10, 9, 12, 9. Find $$Q_1$$, $$Q_2$$, and $$Q_3.$$

Accepted Answer

$$Q_1 = 9$, Q_2$ = 11.5$$, $$Q_3 = 14.5$

Question 10

Suppose a student is randomly chosen from a college. Let $$A$$ represent the event that the student is enrolled in an arts program. What do $$P(A)$$ and $$P(\overline{A})$$ indicate?

Accepted Answer

$$P(A)$$: The probability that the student is enrolled in art. $$P(\overline{A})$$: The probability that the student is not enrolled in art.

Question 11

A health clinic conducted a 'Rapid Flu' test. Among 135 individuals who tested positive, 22 were false positives. Among 165 individuals who tested negative, 4 were false negatives. What is the probability that a randomly selected individual had a true negative result?

Accepted Answer

0.5367

Question 12

A city was partitioned into small zones of equal area and the number of meteorite strikes per zone was recorded as follows: 0 (120), 1 (45), 2 (20), 3 (10), 4 (5). Estimate the mean number of strikes per zone and round your answer to four decimal places.

Accepted Answer

$$\overline{x} = 0.6550$$

Question 13

In a study of the standard normal distribution, what percentage of the area under the curve falls between $$z = -2$$ and $$z = 2$$?

Accepted Answer

95.0%

Question 14

A university reports that 3.2 percent of its students are international students. If a random sample of 900 students is selected and the proportion of international students in the sample is calculated, what is the mean of the sampling distribution of the sample proportions?

Accepted Answer

0.032

Question 15

For a confidence level of $$c = 0.99$$ and a sample size of $$n = 18$$, find the critical values $$\$$chi^2$$_R$$ and $$\$$chi^2$$_L.$$

Accepted Answer

$$\$$chi^2$$_R = 35.718$$, $$\$$chi^2$$_L = 5.697$$

Question 16

A food scientist wishes to estimate the variability in fiber content (in grams per serving) of a new high-fiber breakfast cereal. A simple random sample of $$n = 36$$ servings yields a sample standard deviation of $$s = 1.20 g. $$Assuming fiber content is normally distributed, using a 99% confidence level, determine the degrees of freedom, the critical values $$\$$chi^2$$_L$$ and $$\$$chi^2$$_R$$, and the confidence interval estimate (up to two decimal places) for the population standard deviation $$\sigma.$$

Accepted Answer

df = 34, $$\$$chi^2$$_L = 16.501$$, $$\$$chi^2$$_R = 58.964$$, 99% CI: $$0.91 \u003c \sigma \u003c 1.72 g$$

Question 17

A juice bottling machine is designed to fill bottles with an average of 600 mL. The machine has a standard deviation of 4 mL. A random sample of 36 bottles shows an average fill of 598.7 mL. The company policy states that the machine must be recalibrated if the sample mean is unusual. Should the machine be recalibrated?

Accepted Answer

No, because the p-value is slightly above 0.05, so the sample mean is not statistically unusual.

Question 18

In a survey of 1050 people, 567 (or 54%) said they were in favor of using AI in diagnosing diseases. A health expert claims the responses might as well be random (like flipping a coin). Given $$P(A) = 0.5$$, $$P(B) = 0.0005 ($$probability of exactly 567 out of 1050 in favor), and $$P(C) = 0.004 ($$probability of 567 or more out of 1050 in favor), is the support of 567 respondents significantly high to refute the expert's claim?

Accepted Answer

Yes

Question 19

Determine the critical $$F-$$value for a right-tailed test at $$\alpha = 0.10$$ with numerator degrees of freedom $$d.f._N = 7$$ and denominator degrees of freedom $$d.f._D = 12.$$

Accepted Answer

2.85

Question 20

A clinician claims that treatment A produces a higher average reduction in symptom score than treatment B at $$\alpha = 0.02. $$Assume independent random samples and normal populations with unequal variances. Data: $$\overline{x}_1 = 15.2$$, $$s_1 = 2.5$, n_1$ = 18$$; $$\overline{x}_2 = 13.6$$, $$s_2 = 1.8$, n_2$ = 20. $$What is the correct conclusion?

Accepted Answer

There is insufficient evidence at the $$\alpha = 0.02$$ level to support the clinician's claim that treatment A produces a higher average reduction in symptom scores than treatment B.

Dot Plots: Interpreting Coffee Consumption Data

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