Biostats

what is p value

.0209 or .021

input the upper bound

.029

Which hypothesis involves equality (=)?

the null hypothesis

There are two types of errors that can be made when performing a hypothesis test. Which one involves rejecting the null hypothesis when the null hypothesis is true?

type one

Which of the following is the test statistic, as defined when sigma is known

z test

Which of the following would be the appropriate null hypothesis, Ho The average claim amount is equal to $1,500. The average claim amount is not equal to $1,500. The average claim amount is greater than $1,500. The average claim amount is less than $1,500.

The average claim amount is equal to $1,500

Use the following information to answer the next 6 questions. Accupril is meant to control hypertension. In clinical trials of Accupril, 2142 subjects were divided into two groups. The 1563 subjects in the experimental group received Accupril. The 579 subjects in the control group received a placebo. Of the 1563 in the experimental group, 61 experienced dizziness as a side effect. Of the 579 subjects in the control group, 15 experienced dizziness as a side effect. Let LaTeX: p_1 p 1 be the true proportion of people who experience dizziness while taking Accupril. Let LaTeX: p_2 p 2 be the true proportion of people who experience dizziness but do not take Accupril. Create a 95% confidence interval for p_1-p_2 p 1 − p 2 . Input the lower bound.

-.003

the p-value of your test is

.145

input the upper

.31

Is there sufficient evidence to conclude that the true proportion of people who experience dizziness while taking Accupril is different than the true proportion of people who experience dizziness while not taking Accupril? 1 No. I failed to accept H a 2 Yes. I accepted H a 3No. I rejected H 0 4Yes. I failed to reject H 0 5Yes. I rejected H 0 6No. I failed to reject H 0

6

Suppose the null hypothesis is μ=10. Use this information to answer the next three questions. Which of the following represents the alternative hypothesis for a two-tailed test? Ha: u<10 Ha: u> 10 Ha: u /=10 Ha: u=10

c

In another school a similar sample of student SAT math scores was taken. The principal of that school also believed that his students scored better than the national average. Suppose this principal collected a simple random sample of student SAT scores in math. The sample data collected had a mean student SAT score higher than 550 and the calculated P-value indicated that the null hypothesis should be rejected. In fact, the true population mean of that school's students' SAT scores is the same as the national mean score. What kind of error has been committed and why? Type I error because the principal rejected the null hypothesis when it was true. Type I error because the principal failed to reject the null hypothesis when it was true. Type II error because the principal rejected the null hypothesis when it was true. Type II error because the principal failed to reject the null hypothesis when it was true.

Type I error because the principal rejected the null hypothesis when it was true.

What is your conclusion for this problem? We have insufficient evidence that the true population mean is 150. We have sufficient evidence that the true population mean is 150. We have insufficient evidence that the true population mean is less than 150. We have sufficient evidence that the true population mean is less than 150

We have insufficient evidence that the true population mean is less than 150.

What is the standard deviation of the distribution of the sample proportions?

.046

If α=0.05, compute the probability of committing a Type I error. (Round to two decimal places) 0.05

.05 because the level of signigance (a) is the probability of committing a type 1 error

Calculate the P-value for this hypothesis test. Assume the requirements for the test are satisfied.

.087

What is the probability that your random sample of 100 adults will have a sample proportion less than 0.25?

.138

Use the following information to answer the next 8 questions. A recent book noted that only 20% of all investment managers outperform the Dow Jones Industrial Average over a five-year period. A random sample of 200 investment managers that had graduated from one of the top ten business programs in the country were followed over a five-year period. Fifty of these outperformed the Dow Jones Industrial Average. Let p be the true proportion of investment managers who graduated from one of the top ten business programs who outperformed the Dow Jones over a five-year period. Based on the results of the sample, create a 95% confidence interval of p Input the lower bound.

.19

Use the following information to answer the next three questions. You take a simple random sample of 100 adults from a town in the Western United States to determine the proportion of those in town who invest in the stock market. Assume the unknown population proportion or percentage of people in town who invest in the stock market is p=0.30 p = 0.30 (or 30%). What is the mean of the distribution of the sample proportions?

.3

DoubleStuf Oreo cookies are supposed to have twice the filling of regular Oreo cookies. You and some friends decide you want to know if that is a true assertion by the company who makes them. You take a sample of 55 DoubleStuf Oreo cookies and measure the amount of filling in each one. You need to construct a confidence interval to estimate the true mean filling amount of DoubleStuf Oreos in order to compare it to the filling amount in regular Oreos. Which confidence interval would be most appropriate for this study?

1 sample t confidence interval

Suppose you create a 95% confidence interval for a mean, and get (10, 20). You've been told to report this by saying something like, "We are 95% confident that the true mean is between 10 and 20." Exactly what does this mean? 1 95% of the sample means are between 10 and 20. 2 95% of all 95% confidence intervals actually contain the true mean. 3 95% of the data are between 10 and 20. 4 There is a 95% chance that the true mean is between 10 and 20.

2

What do you conclude based on your results? 4 We have sufficient evidence to say that being a morning or evening person is not independent of age. 1 We have sufficient evidence to say that being a morning or evening person is independent of age. 2 We have insufficient evidence to say that being a morning or evening person is independent of age. 3 We have insufficient evidence to say that being a morning or evening person is not independent of age.

3

Which one of the following best defines the notion of the P-value of a hypothesis test? 1. The probability of the type I error. 2. The probability of the type II error. 3. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. 4. The probability of rejecting H 0 , whether it's true or not.

3

Use the following information to answer the next 4 questions. A survey was conducted of 1382 randomly selected adults aged 18 and older. They were asked "Are you a morning person or a night person?" The hypotheses for this study are: H 0 Being a morning or evening person is independent of age. H a Being a morning or evening person is not independent of age. The results of the survey are given here. Conduct a test of independence. Use a level of significance of α = 0.05 Input the value of the test statistic below.

6.579

What inference would you make about the null hypothesis for this problem?

FAIL TO REJECT

Suppose you're conducting a hypothesis test for one mean, the significance level is α = 0.05 , and the P-value is 0.30. Should you reject or fail to reject Ho and why?

Fail to reject because the P-value is greater than the significance level.

Which of the following represents the alternative hypothesis for a left-tailed test? Ha: u<10 Ha: u> 10 Ha: u /=10 Ha: u=10

Ha: u<10

Which of the following represents the alternative hypothesis for a right-tailed test? Ha: u<10 Ha: u> 10 Ha: u /=10 Ha: u=10

Ha: u> 10

An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,500. They are concerned that the true mean is actually higher than this. Use this information for the next two questions. Which of the following would be the appropriate alternative hypothesis, Ha?

Ho u=1,500 Ha: u> 1,500 The average claim is greater than 1,500

Use the following information to answer the next 4 questions. The national mean SAT score in math is 550. Suppose a high school principal claims that the mean SAT score in math at his school is better than the national mean score. A random sample of 72 students finds a mean score of 574. Assume that the population standard deviation is σ = 100 . Is the principal's claim valid? Use a level of significance of α = 0.05 . State the null and alternative hypotheses.

Ho: u=550 Ha: U>550

The true mean hours of sleep a night of college students in the United States is 6.2 hours. Suppose you want to use a hypothesis test to determine whether the mean hours of sleep a night of BYU-Idaho students is higher than the national mean. Which of the following pairs of hypotheses is the most appropriate for addressing this question?

Ho=6.2 Ha u>6.2

The insurance company randomly selects n=40 claims, and calculates a sample mean of {x}=$1650 . Use this information to answer the next three questions. The insurance company assumes the distribution of the sample mean is normal. Is this a good assumption? It is a good assumption since the sample size is large It is not a good assumption since the sample size is small It is a good assumption since the population is normal It is not a good assumption since the population is not normal. It is not a good assumption since the sample size is small It is a good assumption since the population is normal It is not a good assumption since the population is not normal.

It is a good assumption since the sample size is large

Should you reject H 0 or not? Explain.

No. The P-value is greater than 0.05.

Which relationship would result in reject the null hypothesis? P>a P<a P>z P,z

P<a

Which relationship would result in failing to reject the null hypothesis? P>a P<a P>z P,z

P>a

A researcher decided that instead of using a level of significance of α=0.05, he will use α=0.01. Which of the following will be true? The probability of a Type I error will increase. The probability of a Type II error will increase. The probability that the null hypothesis is true will decrease. His experiment will be more scientifically valid.

The probability of a Type II error will increase because the α value (the probability of committing a Type I error) is very small, the probability of committing a Type II error will be large

Which one of the following best describes the notion of "the significance level of a hypothesis test?"

The probability of a type I error.

Which one of the following best defines the notion of "the P-value of a hypothesis test?" The probability of a type I error. The probability of a type II error. The probability of rejecting LaTeX: H_0 H 0 , whether it's true or not. The probability of obtaining a test statistic at least as extreme as the one you calculated, assuming the null hypothesis is true.

The probability of obtaining a test statistic at least as extreme as the one you calculated, assuming the null hypothesis is true.

In an article in the Journal of Small Business Management, successful start-up businesses in the United States and Korea were compared. One set of data compared educational level (high school, undergraduate degree, master's degree, doctoral degree) of people who managed successful start-up companies in the United States and Korea. You want to determine if education level of managers of successful start-up companies is independent of the country they are from (United States and Korea). Which hypothesis test would be most appropriate for this analysis?

chi-squared test of independence

In a Wall Street Journal article on satisfaction with career paths, the percentage of psychology majors reporting they were "satisfied" with their career path was reported. The same data was also reported for accounting majors. You decide to construct a 95% confidence interval to see if the observed difference is significant. Which confidence interval would be most appropriate for this study

confidence interval for two propotion

A student project compared the effectiveness of two different combination locks. One of the locks turned clockwise first and the other lock turned counterclockwise first. They asked 25 students to participate in the study. Each student was given the combination to each lock and asked to open the locks. The time it took them to open each lock was recorded. They want to determine if one of the locks is easier to open. Which hypothesis test would be most appropriate for this analysis?

paired sample t-test

A bank employs two appraisers. When approving borrowers for mortgages, it is imperative that the appraisers value the same types of properties consistently. To make sure this is the case, the bank evaluates six properties that both appraisers had recently valued. Which confidence interval would be most appropriate for this study?

paired samples t-confidence interval

A survey was conducted by a group of state lotteries. A random sample of 2406 adults completed the survey. A total of 248 were classified as "heavy" players. Of these, 152 were male. You want to determine if the proportion of male "heavy" lottery players is different than the proportion of males in the population, which is 48.5%. Which hypothesis test would be most appropriate for this analysis?

test of one proportions

A human resources manager reported data from a recent involuntary Reduction in Force (RIF) at her company. You are an attorney and want to determine if age discrimination was a factor (it is illegal to discriminate against employees because of age). The company reported the number of employees in two groups: 40 years old or younger, and over 40 years old. They also reported the number of employees in each group who were terminated. You want to determine if both age groups were treated equally. Which hypothesis test would be most appropriate for this analysis?

test of two proportions

Which one of the following best defines the notion of the significance level of a hypothesis test? 1. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true 2. The probability of committing a Type I error 3. The probability of rejecting H 0 , whether or not it is true 4. The probability of committin . Type II error

the probability of committing a type 1 error

What is the P-value associated with the z-score from the previous question? (Round to three decimal places.)

use normal probability aplet .184

The historical mean of sales receipts at a grocery store is $150 with standard deviation of $40. The store manager suspects that the average has decreased. She sets up a hypothesis test with the hypotheses Ho: u=150 Ha: u<150 She will use a level of significance of α=.05. She then takes a simple random sample of 36 sales receipts from her store and computes x=$144. Use this information to answer the next four questions. What is the z-score associated with this test? (Round to three decimal places)

x=144 o=40 a=.5 n=36 u=150 z=x-u/osquareroot of n -.9

Compute the test statistic for this analysis. Round your answer to 3 decimal places. (Example: 0.398)

z=x-u/osquare root of n z=574-550/100square root of 72 z=2.036

the value of your test statistic

1.458

Remember that the P-value is the probability of obtaining a sample statistic at least as extreme as the one that was actually observed. When computing the P-value, which hypothesis do you assume to be true?

Null hypothesis

What theorem or law justifies your answer to the previous question? Law of Large Numbers Central Limit Theorem Law of Total Probability

central limit therum

how is Pvalue calculated

the area under the normal distribution curve that is more extreme (farther away from the mean) than the z-score. The alternative hypothesis tells us whether we look at both tails or only one.