Q: A researcher is interested in the mean salary for software engineers with a bachelor's degree in 2024. A random sample of 24 software engineers was taken, and the sample mean salary was $$\bar{x} = \85$$,500$$ with a sample standard deviation of s$$ = \$$12,000. $$What is the 95% confidence interval for the mean salary?

$$85,500 \pm 2.064 \times \frac{12,000}{\sqrt{24}}$$

Q: A study was conducted to compare the effectiveness of two different fertilizers on corn yield. Fertilizer A: $$n = 36$$, sample mean $$= 104$$ bushels, sample standard deviation $$= 8$$ bushels. Fertilizer B: $$n = 36$$, sample mean $$= 98$$ bushels, sample standard deviation $$= 10$$ bushels. What is the 99% confidence interval for the difference in mean corn yield between Fertilizer A and Fertilizer B?

$$(104 - 98) \pm 2.576 \times \sqrt{\frac{8^2$}{36} + \frac{10^2$}{36}}$$

Question 1

A university wants to estimate the general health and exercise habits of its students. They randomly select 200 students from their enrollment list of 20,000 students and survey them. What is the population in this study?

Accepted Answer

All students enrolled at the university

Question 2

Which of the following variables is quantitative?

Accepted Answer

The number of siblings in a family

Question 3

A scientist wants to test if a new medication reduces the appearance of wrinkles. She randomly assigns a group of 100 people to receive the treatment, and another group of 100 to receive a placebo. What is the purpose of the placebo group in this experiment?

Accepted Answer

To measure the effect of the medication compared to no treatment

Question 4

A gym instructor recorded the number of minutes 12 different members spent on the treadmill: 62, 72, 74, 78, 81, 85, 88, 91, 95, 98, 104, 102. What is the median number of minutes spent?

Accepted Answer

$$\frac{88 + 91}{2} = 89.5$$

Question 5

An automobile battery manufacturer claims that its batteries have a population mean life of $$\mu = 48$$ months with a population standard deviation of $$\sigma = 4$$ months. A quality control manager takes a random sample of $$n = 36$$ batteries. What is the standard error of the mean battery life for the sample?

Accepted Answer

$$\frac{4}{\sqrt{36}} = 0.667$$

Question 6

Researchers measured the total weekly study time in hours and the final exam score (out of 100) for several students. The correlation coefficient $$r$$ between study time and exam score is $$0.93. $$What does this value of $$r$$ indicate?

Accepted Answer

There is a strong positive linear relationship between study time and exam score

Question 7

In a recent semester at a local university, 400 students enrolled in both Biology and Chemistry. Of these students, 60 got an A in Biology, 90 got an A in Chemistry, and 50 got an A in both Biology and Chemistry. What is the probability that a randomly chosen student got an A in Biology or Chemistry?

Accepted Answer

$$\frac{60 + 90 - 50}{400} = 0.25$$

Question 8

Which statement about the standard deviation is correct?

Accepted Answer

If all the data values are exactly the same, then the standard deviation will be zero

Question 9

A researcher is interested in the mean salary for software engineers with a bachelor's degree in 2024. A random sample of 24 software engineers was taken, and the sample mean salary was $$\bar{x} = \85$$,500$$ with a sample standard deviation of s$$ = \$$12,000. $$What is the 95% confidence interval for the mean salary?

Accepted Answer

$$85,500 \pm 2.064 	imes \frac{12,000}{\sqrt{24}}$$

Question 10

A study was conducted to compare the effectiveness of two different fertilizers on corn yield. Fertilizer A: $$n = 36$$, sample mean $$= 104$$ bushels, sample standard deviation $$= 8$$ bushels. Fertilizer B: $$n = 36$$, sample mean $$= 98$$ bushels, sample standard deviation $$= 10$$ bushels. What is the 99% confidence interval for the difference in mean corn yield between Fertilizer A and Fertilizer B?

Accepted Answer

$$(104 - 98) \pm 2.576 	imes \sqrt{\frac{8^2$}{36} + \frac{10^2$}{36}}$$

Question 11

A light bulb company claims its new LED bulbs last more than 40,000 hours. A simple random sample of 20 bulbs yields a sample mean of 41,200 hours and a sample standard deviation of 2,400 hours. What is the value of the test statistic for testing the company's claim?

Accepted Answer

$$\frac{41,200 - 40,000}{2,400 / \sqrt{20}}$$

Question 12

Which of the following best describes the sampling distribution of the sample mean for a sufficiently large sample size?

Accepted Answer

It is approximately normal, regardless of the population distribution

Question 13

A clinical trial tests a new drug and finds a statistically significant reduction in blood pressure compared to a placebo group. What does 'statistically significant' mean in this context?

Accepted Answer

The observed reduction in blood pressure is unlikely to have occurred by chance alone

Question 14

Which of the following is NOT a reason to use random sampling in a study?

Accepted Answer

To guarantee that the sample mean equals the population mean

Question 15

If the probability of an event is impossible to occur, what is its probability?

Accepted Answer

$$0$$

Question 16

A researcher wants to test the hypothesis that the mean salary for software engineers with a bachelor's degree is $$\90$$,000$$. The sample mean is $$\$$85,500$$ and the sample standard deviation is $$\12$$,000$$ for n = 24$. What is the null hypothesis H_0$?

Accepted Answer

$$H_0$$: \mu = 90,000$$

Question 17

Which of the following statements about correlation is correct?

Accepted Answer

A correlation coefficient of $$r = 0$$ means there is no linear relationship between the variables

Question 18

A battery manufacturer claims the mean battery life is 48 months. A sample of 36 batteries has a mean of 46 months and a standard deviation of 4 months. What is the value of the test statistic for testing the manufacturer's claim?

Accepted Answer

$$\frac{46 - 48}{4 / \sqrt{36}}$$

Statistics Final Exam Study Guide: Key Concepts and Applications

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