Q: A new instructor wants to estimate the mean grade of her statistics class. She takes a random sample of $$7$$ students with a mean of $$77.0$$ and standard deviation of $$3.1. $$What is the $$95\%$$ confidence interval for the mean?

$$77.0 \pm t_{0.025,6} \times \frac{3.1}{\sqrt{7}}$$

Question 1

Which of the following variables is a quantitative discrete variable?

Accepted Answer

Number of days of rainfall in a month

Question 2

A manager wants to estimate the average typing speed of current employees. Which of the following best describes the population in this scenario?

Accepted Answer

All current secretaries in the company

Question 3

Which of the following is a parameter?

Accepted Answer

The proportion of all students who own cell phones

Question 4

A survey of 16 households records the number of televisions in each. What type of variable is this?

Accepted Answer

Quantitative discrete

Question 5

Given the following pulse rates for 9 students: 81, 82, 83, 84, 85, 86, 87, 88, 89. What is the median pulse rate?

Accepted Answer

$$85$$

Question 6

Which measure of location is least affected by outliers?

Accepted Answer

Median

Question 7

For the data set $$x = \{2, 4, 6, 8, 10, 13, 18\}$$, what is the linear correlation coefficient $$r$$ between $$x$$ and $$y if$$ $$y = x$$?

Accepted Answer

$$r = 1$$

Question 8

A university parking lot survey found 135 cars from Europe, 124 from Asia, and 131 from America. If a car is picked at random, what is the probability it is from Asia?

Accepted Answer

$$\frac{124}{390}$$

Question 9

Suppose each customer entering an electronics store has a $$35\%$$ chance of making a purchase. If 12 customers enter, what is the probability that at least 3 make a purchase?

Accepted Answer

$$1 - \sum_{k=0}^{2} \binom{12}{k} (0.35)^k (0.65$$)^{12-k}$$

Question 10

During August in Jacksonville, noon-time humidity levels are normally distributed with a mean of $$60$$ and standard deviation of $$2.3. $$What is the probability that a randomly selected day will have a humidity level less than $$57$$?

Accepted Answer

$$P(Z \u003c \frac{57-60}{2.3})$$

Question 11

A bank’s credit card holders have balances with a mean of $$502$$ and standard deviation of $$57. If $$you randomly select $$200$$ accounts, what is the standard deviation of the mean balance in the sample?

Accepted Answer

$$\frac{57}{\sqrt{200}}$$

Question 12

A sample proportion is used to estimate the population proportion. Which formula gives the standard deviation of the sample proportion $$\hat{p}$$?

Accepted Answer

$$\sqrt{\frac{p(1-p)}{n}}$$

Question 13

A new instructor wants to estimate the mean grade of her statistics class. She takes a random sample of $$7$$ students with a mean of $$77.0$$ and standard deviation of $$3.1. $$What is the $$95\%$$ confidence interval for the mean?

Accepted Answer

$$77.0 \pm t_{0.025,6} 	imes \frac{3.1}{\sqrt{7}}$$

Question 14

A large order company tests $$5,000$$ can openers and finds $$112$$ defective. Test the claim that the proportion of defective can openers is less than $$2\%$$ using $$\alpha = 0.01. $$What is the null hypothesis?

Accepted Answer

$$H_0$$: p = 0.02$$

Question 15

A farm tests a new procedure to increase corn yield. The average yield before was $$127$$ bushels/acre. After the procedure, a sample of $$16$$ fields has a mean yield of $$131$$ and standard deviation $$5. $$What is the test statistic for testing if the new procedure increased yield?

Accepted Answer

$$t = \frac{131 - 127}{5/\sqrt{16}}$$

Question 16

Which of the following best describes a binomial experiment?

Accepted Answer

Each trial has only two possible outcomes and trials are independent

Question 17

If the sample mean is $$\bar{x}$$ and the population mean is $$\mu$$, which formula gives the $$z-$$score for $$\bar{x} in a $$sampling distribution?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$$

Question 18

Which graphical display is most appropriate for showing the relative frequency distribution of the number of televisions in households?

Accepted Answer

Histogram

Question 19

Given a normal distribution with mean $$\mu = 60$$ and $$\sigma = 2.3$$, what is the $$z-$$score for a humidity level of $$64$$?

Accepted Answer

$$z = \frac{64 - 60}{2.3}$$

Comprehensive Final Exam Review for Introductory Statistics

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