Hypothesis Testing and Confidence Intervals in Statistics | Exams Data Analysis & Statistical Methods

1. Two brands of cornflakes both print on the box that they weigh 12 oz. However, you believe that, on

average, Brand A weighs more than Brand B. What is the alternative hypothesis that you are testing?

a. μ



b. pA > pB

xx 

pp ˆˆ 





2. Which of the following is true according to the Central Limit Theorem?

a. If the population distribution is normal, the sample size must be large for the distribution of

the sample means to be normal.

b. If the population distribution is skewed, the distribution of the sample variances is normal if

there is a large sample size.

c. If the population distribution is not normal, the distribution of the sample means is normally

distributed as long as np and n(1-p) are both greater than 10.

d. If the population distribution is normal, the distribution of sample variances is normal

regardless of sample size.

e. None of the above is true.

3. A recent study asked a random sample of 2000 shoppers in a particular grocery store if they thought that

the checkout lines were too long. Suppose that 64% of all shoppers would agree to this question. Then

what is the approximate distribution of the count of people who say yes, the X’s?

a. X ~ N(1280, 21.472)

b. X ~ N(.64, .01072)

c. X ~ N(1280, .460.82)

d. X ~ N(1280, .00012)

e. The assumptions are not satisfied, so we cannot determine the approximate

distribution.

4. Suppose that a national achievement test is given to 10th graders each year. It has a mean score of 200

and a standard deviation of 15. What is the probability that a randomly selected group of 25 students has a

mean score greater than 195?

a. .0475

b. .9525

c. .6293

d. .3707

e. None of the above are true

5. A manufacturer of laundry soap labels bottles as containing 15 oz. A sample of 15 bottles is taken off of

the manufacturing line. The sample is found to have a mean of 15.2 oz and a standard deviation of .25 oz.

The researcher wants to know if the mean weight of the bottles is actually more than 15 oz. (Suppose we

know that the weights are normally distributed.) Which is the appropriate test to run?

a. a 1 sample z test (#1) since the weights are normal

b. a 1 sample z test for proportions (#6) with

being the proportion of bottles weighing

more than 15 oz.

c. a 1 sample t test (#2) since we don’t know the population variance

d. a 2 sample t test (#9) comparing the bottles weighing more than 15 oz to those with

less than 15 oz.

e. a nonparametric test (NP) since we have a sample size less than 30.

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Two brands of cornflakes both print on the box that they weigh 12 oz. However, you believe that, on average, Brand A weighs more than Brand B. What is the alternative hypothesis that you are testing?

a. μ  12

b. pA > pB

c. x^ A  xB

d. p ˆ A  p ˆ B

e.  A   B

Which of the following is true according to the Central Limit Theorem? a. If the population distribution is normal, the sample size must be large for the distribution of the sample means to be normal. b. If the population distribution is skewed, the distribution of the sample variances is normal if there is a large sample size. c. If the population distribution is not normal, the distribution of the sample means is normally distributed as long as np and n(1-p) are both greater than 10. d. If the population distribution is normal, the distribution of sample variances is normal regardless of sample size. e. None of the above is true.
A recent study asked a random sample of 2000 shoppers in a particular grocery store if they thought that the checkout lines were too long. Suppose that 64% of all shoppers would agree to this question. Then what is the approximate distribution of the count of people who say yes, the X’s? a. X ~ N(1280, 21.47^2 ) b. X ~ N(.64, .0107^2 ) c. X ~ N(1280, .460.8^2 ) d. X ~ N(1280, .0001^2 ) e. The assumptions are not satisfied, so we cannot determine the approximate distribution.
Suppose that a national achievement test is given to 10th^ graders each year. It has a mean score of 200 and a standard deviation of 15. What is the probability that a randomly selected group of 25 students has a mean score greater than 195? a.. b.. c.. d.. e. None of the above are true
A manufacturer of laundry soap labels bottles as containing 15 oz. A sample of 15 bottles is taken off of the manufacturing line. The sample is found to have a mean of 15.2 oz and a standard deviation of .25 oz. The researcher wants to know if the mean weight of the bottles is actually more than 15 oz. (Suppose we know that the weights are normally distributed.) Which is the appropriate test to run? a. a 1 sample z test (#1) since the weights are normal b. a 1 sample z test for proportions (#6) with p ˆ^ being the proportion of bottles weighing more than 15 oz. c. a 1 sample t test (#2) since we don’t know the population variance d. a 2 sample t test (#9) comparing the bottles weighing more than 15 oz to those with less than 15 oz. e. a nonparametric test (NP) since we have a sample size less than 30.

You are getting ready to buy a new television and can’t decide which size to buy. Then you see an article that says that they have done a 2 sample t-test and concluded that there is not significant evidence to show that the mean price of 27 inch televisions is greater than the mean price of 25 inch televisions. They report a p-value of .07. Which of the following is true? a. It is possible that the significance level, α, used for the test was .05. b. From the information given, we can tell that the power of the test was .93. c. A Type I Error could have been committed. d. Two of the answers a, b, and c are true. e. All of answers a, b, and c are true
Suppose we are conducting a test of H 0 : p=.5 vs. Ha: p > .5 and we get a p-value of .05. The sample size used in our test was n=21. Which of the following was the test statistic that was calculated from this data? a. z = -1. b. t = 1. c. z = 1. d. t = 1. e. t = -1.
In class, we looked at some examples about the difference in prices (in dollars) of one and two bedroom apartments. Suppose we construct a 95% confidence interval for μ 2 – μ 1 (where μ 2 is the mean price of 2 bedroom apartments and μ 1 is the mean price of one bedroom apartments) and get an interval of 75 ± 69. Which of the following is true? a. We can say that there is a 95% probability that the true difference in means is in between $ and $144. b. We know that the in the samples that were collected in order to construct this confidence interval, the sample mean for two bedroom apartments was exactly $75 more than the sample mean for one bedroom apartments. c. Since this interval does not include 0, we know that there are no one bedroom apartments that are more expensive than two bedroom apartments. d. If we wanted a narrower interval, we could construct a 99% confidence interval instead. e. Two of the above are true.
A paired t-test (matched pairs t-test) is run to see if, on average, baseballs hit with metal bats go farther than baseballs hit with wooden bats, i.e., H 0 : μM = μW vs. Ha: μM > μW. 20 baseball players are used to conduct this study. A p-value of .03 is obtained. Which of the following is FALSE? a. The power of this test would be increased if 30 baseball players were involved in the study. b. A Type II Error would happen if we conclude that baseballs hit with metal and wooden bats go the same distance when, in reality, baseballs hit with metal bats do travel farther on average. c. To conduct this test we will have 10 baseball players hit with wooden bats and the other 10 hit with metal bats. Then we will pair the data and subtract the distances from each other. Then we will run a regular one sample t-test. d. At an α level of .01, it is not possible to make a Type I Error. e. At an α level of .05, we would conclude that, on average, balls hit with metal bats go farther than balls hit with wooden bats.
We want to conduct a 90% confidence interval for the proportion of juniors at A&M who have taken STAT 303. We do not know what the population proportion, p, is so we can use .5 as our guess. If we want the width of the interval to be .05, i.e. we want the interval to look like estimate ± .025, what sample size will we need to use? a. 13 b. 14 c. 1078 d. 1079 e. 267

A research team wants to estimate the proportion of students who will attend graduate school after they receive their first college degree. Out of 300 undergraduate students questioned, 22% responded that they were planning to continue their education with graduate school. Use this information to construct a 99% confidence interval for p. (5 pts.) Based on this interval, would you reject or fail to reject the null hypothesis, in the test of H 0 : p=.25 vs Ha: p≠.25 at the .01 significance level? State your conclusion. (5 pts.)

An agricultural researcher plants 25 plots with a new variety of corn. The average yield of these plots

is x  150 and the standard deviation of these plots is 20. The researcher wants to see if the mean yield

of the new variety of is significantly different from 140 and the .01 significance level. Step 1: State the null hypothesis. (1 pt.) Step 2: State the alternative hypothesis. (1 pt.) Step 3: State the α level. (1 pt.) Step 4: Calculate the test statistic. (2 pts.) Step 5: Calculate the p-value. (2 pts.) Step 6: Reject or Fail to Reject the null hypothesis and give your reasoning. (2 pts) Step 7: State your conclusion in terms of the problem. (1 pts) Step 8 (3 points bonus) State whether a type I error, type II error or both are possible based on the above test and what it (or they) mean in terms of the problem.

Hypothesis Testing and Confidence Intervals in Statistics, Exams of Data Analysis & Statistical Methods

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