Prob&Stats

Use scenario 6-4. The expected payoff per card is

$.85

The weights of a sample of three adult males are (in pounds) 160, 215, and 195. The standard error of the mean of these three weights is

16.07

What is the critical value t* for a 99% confidence interval when n=20?

2.861

A corporation with several thousand employees wants to estimate the mean commute time for all employees. They would like to construct a 95% confidence interval with a margin of error of no more than 4 minutes. Preliminary interviews with a small sample suggest that a reasonable estimate of the population standard deviation is 10 minutes. Which of the following is the smallest sample of the company can take to achieve the desired margin of error?

25

Assume that the change on SAT-M score (second score-first score) for the population of all students taking the test twice is approximately Normally distributed with mean mu. A 90% confidence interval for mu is

25.0 +/- 47.56

Use scenario 6-5. Use the mean number of customers that make a purchase during the first hour that the store is open is

3.0

A college basketball player makes 5/6 of his free throws. Assuming free throw attempts are independent, the probability that he makes exactly three of his next four free throws is

4(1/6)^1(5/6)^3

I roll a pair of fair dice and let X=the sum of the spots on the two sides facing up. The probability that X is 2,11, or 12 is

4/36

Use scenario 6-11. What is the standard deviation of T? (Assume the lengths of the songs are independent.)

5.37

Use scenario 6-17. On average, how many people do you expect you will have to ask before you find someone with jumper cables?

6.25

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of no more than $2, and the amount spent has an approximately Normal distribution with a standard deviation=$30. The number o observations required closest to

609

Which of the following confidence intervals has the largest critical value?

A 95% t-interval with 1 degree of freedom.

You test the hypothesis Ho: mu=1 against the alternative Ha: mu=/1 and obtain a P-value of 0.022. Which of the following must be true?

A 99% confidence interval for mu will include the value 1

Use scenario 7-2. The statistic that has the lowest variability among these three is

B and C have similar variability, and it is less than the variability of A.

According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let's assume this is the parameter value for the population. Suppose you increased the sample size to n=50 Americans and let p(hat)= the proportion in the sample who get 30 minutes of exercise at least five days per week. How would the sampling distribution of p(hat) compare to the sampling distribution for n=25?

Center would be the same, spread would be smaller for n=50, and only the shape for the larger sample would be approximately Normal.

Use scenario 6-4. The probability that a random scratch-card will pay off is

.0601

The weight of written reports produced in a certain department has a Normal distribution with mean 60 g and standard deviation 12 g. The probability that the next report will weight less than 45 g is

.1056

A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed 60 times. The probability that less than 1/3 of the tosses are heads is closest to

0.0049

Use scenario 6-17. You're going to give up and call a tow truck if you don't find jumper cables by the time you've asked 10 people. What's the probability you end up calling a tow truck?

0.1749

An automobile insurer has found that repair claims have a mean of $920 and a standard deviation of $870. Suppose that the next 100 claims can be regarded as a random sample from the long-run claims process. The probability that the mean of the next 100 claims is larger than $1000 is approximately

0.1788

Use scenario 6-8. The value of P(X>$400) is

0.2119

According to a recent poll, 27% of Americans get 30 minutes of exercise at least fiver days each week. Let's assume this is the parameter value for the population. If a simple random sample of size n=50 were taken, what is the approximate probability that p(hat), the proportion who exercise at least five days per week, is higher than 0.30?

0.3164

Use scenario 8-3. A 95% confidence interval for p is

0.64 +/- 0.094

Use scenario 6-1. The probability of at least one tail is

0.9375

In their advertisements, a new diet program would like to claim that their methods result in a mean weight loss of more than ten pounds in two weeks. In order to determine if this is a valid claim, they hire an independent testing agency that then selects twenty-five people to be placed on this diet. The agency is testing the null hypothesis:mu=10. Which of the following is the correct alternative hypothesis?

Ha: mu>10

To determine if having children within the first two years of marriage increases the divorce rate, where p=proportion of marriages that end in divorce, which one of the following sets of hypotheses should we test?

Ho: p=0.5; Ha: p>0.5

I wish to test the hypothesis Ho: mu=5 versus Ha: mu=/5 based on an SRS if size n from a Normal population. I calculate 95% confidence interval for mu and find it to be 1.33 to 4.67. Which of the following is true?

I would reject Ho at level .05

A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes (P=0.287). Which of the following is correct interpretation of this value?

If in fact there is no difference in mean GPAs, the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample is 0.287.

Suppose a large population has mean and standard deviation, and a simple random sample of size n is taken Which one of the following gives the correct formulas for mean and variance of the sampling distribution of the mean?

Mean=mu; Variance= standard deviation^2/n

A marketing company discovered the following problems with a recent poll: 1. Some people refused to answer questions 2. People without telephones could not be in the sample 3. Some people never answered the phone in several calls Which of these sources is included in the +/-2% margin of error announced for the poll?

None of these sources of error.

In testing hypotheses, which of the following would be strong evidence against the null hypothesis?

Obtaining data with a small P-value

Use scenario 6-1. An expression that represents the probability of at least one tail is

P(z</=3)

An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence interval for the average yield for these plots if found to be 162.72 +/- 4.47 bushels per acre. Which of the following would produce a confidence interval with a smaller margin of error than this one?

Planting 100 plots, rather than 25.

Which of the following random variables should be considered continuous?

The height of a randomly chosen adult female.

A website asks visitors to vote for which of several user-submitted video is funniest. After a few days they have collected 250 votes, and they would like to construct a 95% confidence interval for the proportion of visitors who prefer one of the videos. However, they recognize that their sampling method involves voluntary response, so the data may be biased. How can they compensate foe this problem when constructing their confidence interval?

Throw this data out...there is no way to compensate for this bias.

In 2011, 2.6% of all vehicles registered in California were motorcycles. In a random sample of 300 vehicles entering Yosemite National Park that year, 12 of them were motorcycles. In this evidence (at the alpha=0.05 level) that the percentage of motorcycles entering the park is higher than the proportion that are registered in California? Which of the following is the correct conclusion for the appropriate test of significance?

We cannot preform this test because the conditions for inference have not been met.

At a school with 600 students, %25 of them walk to school each day. If we choose a random sample of 40 students from the school, is it appropriate to model the number of students in our sample who walk to school with a binomial distribution where n=40 and p=0.25?

Yes, because the sample is less than 10% of the population size.

You are thinking of using a t procedure to estimate the mean of a population using a 95% confidence level. You suspect that the distribution of the population is not normal and may be moderately skewed. Which of the following statement is correct?

You may use the t procedure provided your sample size is large, say at least 30.

I conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level alpha=0.05. I may conclude that

both (A) and (C) are true

Use scenario 9-4. Suppose the mean and standard deviation we obtained were based on a sample of 25 postal workers, rather than 100. The P-value would be

larger

A polling organization announces that the proportion of American voters who favor congressional term limits is 64 percent, with a 95% confidence margin of error of 3 percent. If the opinion poll had announced the margin of error for 80% confidence rather than 95% confidence, this margin of error would be

less than 3%, because we require less confidence

An automobile insurer has found that repair claims have a mean of $920 and a standard deviation of $870. Suppose that the next 100 claims can be regarded as a random sample from the long-run claims process. The mean and standard deviation of the mean of the next 100 claims is

mean= $920 and standard deviation= $87

Twenty-five seniors from a large metropolitan area school district volunteer to allow their Math SAT test scores be used in a study. These twenty-five seniors had a mean Math SAT score of x(bar)= 450 with a standard deviation of s= 100. Assuming that the population of Math SAT scores for seniors in the district is approximatly normally distributed, a 90% confidence interval for the mean Math SAT score mu for the population of seniors computed from this data is

not trustworthy because the conditions for this inference procedure have not been met

The distribution of the value of a variable for all members of a population is

the population distribution of the varaible

The critical value used in 95% confidence interval for a population proportion is

the value in a standard Normal distribution such that 95% of the scores are less that that distance from 0

Here's the quote from a medical journal: "An uncontrolled experiment in 17 women found a significantly improved mean clinical symptom score after treatment. Methodologic flaws make it difficult to interpret the results of this study." The authors of this paper are skeptical about the significant improvement because

there is no control group, so the improvement might be due to the placebo effect or to the fact that many medical conditions improve over time

Use scenario 9-3. The test statistic, P-value, and appropriate decision for this test are:

z=2.40; P-value=0.008;reject Ho

Use scenario 6-12. Which of the following expresses the probability that the students gets no questions correct?

(.8)^20

The distribution of prices for home sales in a certain New Jersey county is skewed to the right with a mean of $290,000 and a standard deviation of $145,000. Suppose you take a simple random sample of 100 home sales from this (very large) population. What is the probability that the mean of our sample is above $325,000?

0.0079

A researcher plans to conduct a test of hypotheses at the alpha=0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type 1 error is

0.01

A college basketball player makes 80% of her free throws. At the end of a game, her team is losing by two points. She is fouled attempting a three-point shot and is awarded three free throws. Assuming free throw attempts are independent, what is the probability that she makes at least two of the free throws?

0.896

In a certain game of chance, your chances of winning are 0.2. If you play the game five times and outcomes are independent, which of the following represents the probability that you win at least once?

1-(0.8)^5

Use scenario 6-5. The standard deviation of the number of customers that make a purchase during the first hour that the store is open is

1.4

Suppose we select an SRS of size n=100 from a large population having proportion p of successes. Let X be the number of successes in the sample. For which value of p would it be safe to assume the sampling distribution of X is approximately normal?

1/9

Use scenario 6-11. What is the expected value of T?

100.0

We wish to see if the dial indicating the oven temperature for a certain model oven is properly calibrated. Four ovens of this model are selected at random. The dial on each is set to 300F, and, after one hour, the actual temperature of each is measured. The temperatures measured are 305F, 310F, 300F, and 305F. Assuming that the actual temperatures for this model when the dial is set to 300F are Normally distributed with mean, we test whether or not the dial is properly calibrated by testing the hypotheses Ho: mu=300, Ha: mu=/300. Which of the following is the value of the test statistic for a one sample t-test?

2.45

Use scenario 8-3. Which of the following is closest to the sample size you would need to estimate p with a margin of error of 0.05 with 95% confidence? Use 0.5 as an approximation of p.

385

An SRS of 100 postal employees found that the average time these employees had worked for the postal service was x(bar)= 7 years with standard deviation s=2 years. Assume the distribution of the time the population of employees have worked for the postal service is approximately Normal. A 95% confidence interval foe the mean time mu the population of postal service employees have spent with the postal service is

7 +/- 0.4

According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let's assume this is the parameter value for the population. If you take a simple random sample of 25 Americans and let p(hat)= the proportion in the sample who get 30 minutes of exercise at least five days per week, is the shape of the sampling distribution of p(hat) approximately Normal?

No, because np<10

A political candidate is told by his polling organization that a 90% confidence interval for the proportion of voters who support his candidacy is 0.45 to 0.53. What are the point estimate and the margin of error for this interval?

Point estimate=0.49; margin of error=0.04

Use scenario 7-2. Based on the performance of the three statistics in many samples, which is preferred as an estimate of the parameter?

Statistic B

You want to determine if the 300 seniors at your school favor a change in location for the senior prom. In order to conduct a test of the hypotheses Ho: p=0.5 against the alternative Ha: p>0.05, you put the names of all the seniors in a hat and draw out 36 names. You find that 25 of the seniors in your sample are in favor of the change. Which one (if any) of the following required conditions for conducting a z-test for a proportion have not been met?

The population is at least 10 times the sample size

Which of the following is not a random variable?

The response of randomly-selected people to the question, "What is your favorite TV sit-com?"

In formulating hypothesis for a statistical test of significance, the null hypothesis is often

a statement of "no effect" or "no difference"

Use scenario 9-4. Which of the following intervals contains the P-value for this test?

between 0.05 and 0.01

The number of classified advertisements appearing on Mondays on a certain online community site has mean of 320 and standard deviation 30. Suppose that the results for 100 consecutive Mondays can be regarded as a simple random sample and let x(bar) denote the mean number of classified advertisement in the sample. Assuming a sample of 100 is sufficiently large, the random variable x(bar) has a

distribution that is approximately normal by the central limit theorem

A buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten. She will only accept the shipment if there is clear evidence that this proportion is less than 0.06. She selects a simple random sample of 200 apples from the over 20000 apples on the truck to test the hypotheses. Ho: p= 0.06; Ha: p < 0.06. The sample contains 9 rotten apples. The P-value of her test is

greater than .10

A random sample of size 25 is to be taken from a population that is Normally distributed with mean 60 and standard deviation 10. The mean x(bar) of the observations in our sample is to be computed. The sampling distribution of x(bar)

is Normal with mean 60 and standard deviation 2

According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let's assume this is the parameter value for the population. If you take a simple random sample of 25 Americans and let P(hat)= the proportion in the sample who get 30 minutes of exercise at least fiver days per week, what are the mean and the standard deviation of the sampling distribution of p(hat)?

mu=0.27;SD: 0.0888

A quality control inspector is testing microprocessor chips made during a single day by a new machine to determine the proportion of defective chips. She selects an SRS of 80 chips from the 3000 chips produced by the machine on that day. It turns out that six of the chips are defective. Which of the following conditions for constructing a confidence interval for the proportion of defective chips has been violated?

np(hat)>/=10 and n(1-p(hat))>/=10

In the 2008 New Hampshire Democratic primary, 30% of voters in a CNN poll said they would vote for Hilary Clinton. Surprisingly, in the primary itself, 39% voted for Clinton. The number 39% is a

parameter

A survey conducted by Black Flag asked whether or not the action of a certain type of roach disk was effective in killing roaches. 79% of the respondents agreed that the roach disk was effective. The number 79% is a

statistic

The most important condition for sound conclusions from statistical inference is usually

that the data can be thought of as a random sample from the population of interest

In a statistical test of significance, we say the data are statistically significant at level alpha if

the P-value is at most alpha

I flip a coin ten times and record the proportion of heads I obtain. I then repeat this process of flipping the coin ten times and record the proportion of heads obtained many, many times. When done, I make a histogram of my results. This histogram approximates

the sampling distribution of the proportion of heads on ten flips of the coin.

If we take many simple random samples from the same population, we expect

the values of the statistic will vary from sample to sample

If a significance test gives a P-value of 0.005

we do have convincing evidence against the null hypothesis