stats 10 final

A claim is made that the proportion of children who play sports is​ 0.5. In a random sample of 400 children,​ 30% said that they play a sport. Find the value of the test statistic z.

-8

Which of the following is an example of theoretical probability? (Select all that apply) -A homeowner notes that five out of seven days the newspaper arrives before 5 pm. He concludes that the probability that the newspaper will arrive before 5 pm tomorrow is about​ 71%. -At a carnival shell game the player can pay three dollars and choose the shell that he or she believes is hiding the prize. There are four shells that are thoroughly mixed up after each guess. The player concludes that there is a one in four chance of randomly picking the winning shell. -A bag contains 2 red​ marbles, 8 blue​ marbles, and 4 green marbles. Adam randomly selected a marble from the​ bag and repeated 50 times. He counted the number of times a blue marble is selected, and claimed that the probability of choosing a blue marble is 40%. -A six-sided die is rolled and a coin is tossed. The probability of getting a tail on the coin and a 2 on the die is​ 8.3%.

-At a carnival shell game the player can pay three dollars and choose the shell that he or she believes is hiding the prize. There are four shells that are thoroughly mixed up after each guess. The player concludes that there is a one in four chance of randomly picking the winning shell.

200 workers at a large company were randomly sampled and asked whether they went on a vacation for at least a week in the past year. A 95% confidence interval was found to be (0.50, 0.66). Which of the following statements are correct about the​ 95% confidence interval from the previous question? -If we use a confidence level of 99% instead of​ 95%, the confidence interval will become wider. -No more than 66% of the workers in the company went on a vacation last year for at least a week. -The population proportion of workers that went on vacation for at least a week in the past year is 0.58. -If the sample size is 500 instead of​ 200 while keeping everything else the same, the confidence interval will be narrower.

-If we use a confidence level of 99% instead of​ 95%, the confidence interval will become wider. -If the sample size is 500 instead of​ 200 while keeping everything else the same, the confidence interval will be narrower.

Suppose the test statistic for a hypothesis test is z = 1.32. What is the appropriate interpretation of test statistic. -It indicates that the result will never be significant, therefore does not provide enough evidence against the null hypothesis. -It indicates that the result is significant at a level of 0.05, therefore provides strong evidence against the null hypothesis. -It indicates that the result could be significant using a​ two-sided alternative hypothesis, therefore provides strong evidence against the null hypothesis indicating. -It indicates that the result is not significant at a level of 0.05, therefore does not provide enough evidence against the null hypothesis.

-It indicates that the result is not significant at a level of 0.05, therefore does not provide enough evidence against the null hypothesis.

Which of the following statements is true about the null hypothesis (H0)? (Select all that apply) -It contains an inequality symbol (e.g., >, <) -It is a statement that represent that something has changed -It is assumed to be true throughout the testing procedure. -It is a statement about the sample statistic -It is a statement that represents no change from the status quo.

-It is assumed to be true throughout the testing procedure. -It is a statement that represents no change from the status quo.

If 20 babies are​ born, how often are there 8 or less male​ babies? Assume that the gender of a baby is a random event with equal chance. Which of the following experiments would not simulate this​ situation

-Roll a die twenty times. Designate a​ 1, 2, or 3 to mean​ "female" and a​ 4, 5, or 6 to mean​ "male". -Randomly draw 20 digits from 1-100. Designate odd numbers to mean​ "female" and even numbers to mean​ "male". -Flip a coin twenty times, Designate a head to mean​ "female" and a tail to mean​ "male".

Which of these is a discrete random variable? -The amount of time it takes you to answer this question. -The number of emails you get per day. -The number of calories contained in a cheese burger. -All of the above

-The number of emails you get per day.

Which of the following is true about a continuous random variable? (Select all that apply) -The variable only takes certain values that can be listed -The sum of all probabilities of individual values is equal to 1 -The probability of any single value is 0 -The probability is measured by the area under the curve

-The probability of any single value is 0 -The probability is measured by the area under the curve

Which of the following statements is correct about the sampling distribution? -The standard deviation of the sampling distribution measures the accuracy of the sample statistic. -The standard deviation of the sampling distribution measures the precision of the sample statistic. -The standard deviation of the sampling distribution measures the precision of the population parameter. -The standard deviation of the sampling distribution measures the accuracy of the population parameter.

-The standard deviation of the sampling distribution measures the precision of the sample statistic.

Suppose that a recent poll of American households with a car found that, 39% owned a sedan, 33% owned a van, and 7% owned a sports car. Suppose that three households are selected independently, what is the probability that all of the three randomly selected households own a van?

0.036

X is a uniformly distributed random variable. The probability density curve is shown below. What is the probability that the variable has a value greater than 6?

0.375

The table below describes the smoking habits of a group of asthma sufferers. NonsmokerLight smokerHeavy smokerTotalMen3936174528Women341 67 78 486Total734 128 152 1,014 If one of the 1,014 subjects is randomly​ selected, find the probability that the person chosen is a nonsmoker given that the person is a woman. Round to three decimal places.

0.702

Three events A, B and C are independent to each other. It is known the probability of event A occurring is 0.2, and the probability of all three event occurring at the same time is 0.18. What is probability of event B and C occurring at the same time? (hint: multiplication rule for independent events)

0.9

Suppose the length of time it takes customers to find a parking spot at a large grocery store parking lot follows a normal distribution with a mean of 7.5 minutes and a standard deviation of 2 minutes. Let X denote the variable length of time. Which of the following will correctly calculate the probability of it taking longer than 9 minutes to find a parking spot? --> 1 - P(z < 0.75) --> 1 - P(x < - 9) --> 1 - P(z < - 0.75) --> P(x < 9) --> P(z < 0.75)

1 - P(z < 0.75)

It is known that a batch of toys produced at a certain factory in a day has a defect rate of 1%. Suppose the quality inspectors randomly inspect 500 toys from the batch and calculate the proportion of defective toys, what will the the sampling distribution look like? The sampling distribution would be centered around ____, with a standard deviation of ____.

5; 0.44%

Which of the following tests will produce the smallest p-value? -A two-sided hypothesis test with a Z-statistic of -0.8 -A right-sided hypothesis test with a Z-statistic of 1.5 -A two-sided hypothesis test with a Z-statistic of 1.5 -A left-sided hypothesis test with a Z-statistic of -0.8

A right-sided hypothesis test with a Z-statistic of 1.5

Which of the following is incorrect about the probability distribution? -The qth percentile of a probability distribution is the value where the area to its left is q%, and the area to its right is (100 − q)%. -A discrete random variable can have countably infinite values -Different probability density curves will have different total area under the curve. -The probability distribution tells us the possible values of a random variable and their associated probabilities

Different probability density curves will have different total area under the curve.

Use your intuition to decide which the following sets of events are likely to be independent. -Event​ A: The randomly selected carton of milk you purchased from the store is sour. Event​ B: Your car​ won't start on a randomly selected morning. -Event​ A: You roll a number larger than four on a die. Event​ B: Rolling a six on a die. -Event​ A: Drawing a club from a deck of cards. Event​ B: Drawing a card with a black symbol from a deck of cards. -Event​ A: A randomly selected person is married with no children. Event​ B: A randomly selected person opposes a tax credit for children.

Event​ A: The randomly selected carton of milk you purchased from the store is sour. Event​ B: Your car​ won't start on a randomly selected morning.

A police radar gun is used to measure the speeds of cars on a highway. Suppose the speeds of cars are normally distributed with mean 60 mph and standard deviation 6 mph. Cars driving at a speed higher than 70 mph might get a speeding ticket. How do you find the proportion of cars that are likely to get a ticket? -Find the probability value associated with -1.67 from the z-table. -Find the probability value associated with -1.87. -Find the probability value associated with -1.87 from the z-table and subtract it from 1 -Find the probability value associated with -1.67 from the z-table and subtract it from 1.

Find the probability value associated with -1.67 from the z-table.

How do you find the z* for a confidence level of 70%?

Find the z value that has a left tail probability of 0.85

Suppose the score of a test follows a normal distribution N(400, 60). How do you find the percentile that separates the top 10% of the test takers from the rest? -Find the z-score that has the closest probability to 0.10 from the z-table and covert it to the test score by calculating 400 + 60*z -Find the z-score that has the closest probability to 0.90 from the z-table and covert it to the test score using 400 + 60*z -Find the z-score that has the closest probability to 0.90 from the z-table and covert it to the test score by calculating 400 - 60*z -Find the z-score that has the closest probability to 0.10 from the z-table and covert it to the test score by calculating 60 + 400*z

Find the z-score that has the closest probability to 0.90 from the z-table and covert it to the test score using 400 + 60*z

Which of the following statements is true about the "Law of Large Numbers" (LLN)? -If an experiment is repeated a large number of times, the empirical probability will be consistently different from the theoretical probability. -If you repeat a random experiment many, many times, the empirical probability should on average approach the theoretical value as the number of trials increase. -If you simulate an experiment that is designed correctly, the empirical probability will always be the same as the theoretical probability that is expected. -If you repeat a random experiment many, many times, your outcomes should be a unique value that is different from the theoretical average.

If you repeat a random experiment many, many times, the empirical probability should on average approach the theoretical value as the number of trials increase.

Previous study showed that the proportion of young adults in the U.S. who reported smoking at least twice a week or more in the last month was 0.15. A researcher is wondering whether the smoking habits of young adults ​(18−25 years of​ age) in a certain city are the same as the general population of young adults in the U.S. The researcher collected data from a random sample of 55 adults in the city of interest and found that 20% of the young adults smoke at least twice a week or more. Check that the conditions hold so that the sampling distribution of the​ z-statistic will approximately follow the standard normal distribution. Are the conditions satisfied? If​ not, choose the condition that is not satisfied. -No, the researcher did not collect a random sample. -No, the researcher did not collect a large enough sample. -No, the population is not large enough -Yes, all the conditions are satisfied.

No, the researcher did not collect a large enough sample.

Which of the following equations can NOT be used to verify that two events are independent? -P(B|A) = P(B) -P(A and B) = P(A)P(B) -P(A or B) = P(A) + P(B) -P(A|B) = P(A)

P(A or B) = P(A) + P(B)

If two events A and B are mutually exclusive, which of the following statements is true? -P(A and B) = P(A)P(B) -A and B are independent -P(A)P(B) = 0 -P(A|B) = 0 -P(A) + P(B) > P(A or B)

P(A|B) = 0

Which of the following is true about the sample statistics? -The statistic is accurate but imprecise if the sample estimates are close to each other but far from the true value. -The statistic is a fixed value. -A statistic is said to be unbiased if it is sampling distribution has a center of 0. -Statistics based on larger sample sizes have smaller standard errors .

Statistics based on larger sample sizes have smaller standard errors .

Which of the following statements about the confidence interval is correct? -The confidence interval contains the population parameter. -The confidence interval is centered at the sample estimate. -The length of the confidence interval is equal to the margin of error. -A higher confidence level gives you more precise estimates.

The confidence interval is centered at the sample estimate.

The distribution of gas consumption for SUVs (mpg) is normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. Another data set for a group of sedans is normally distributed with a center of 28 mpg and a standard deviation of 4 mpg. Which one of the following statements is true when the distributions are compared? -The distribution for the sedans is shifted to the right and not as spread out. -The distribution for the SUVs is shifted to the right and not as spread out. -The distribution for the sedans is shifted to the right and more spread out. -The distribution for the SUVs is centered at the same value as for the sedans but more spread out

The distribution for the sedans is shifted to the right and not as spread out.

Suppose that scores on the verbal portion of the SAT among first-year students at a certain university follow a normal distribution. The mean is about 500 and the standard deviation is about 100. Which of the following statements is correct? -The probability that a randomly selected student scored less than 400 is about 0.05. -The probability that a randomly selected student scored between 500 and 600 is about 0.34. -Andrew's score is in the 95th percentile, so we know his score is 700. -John scored 490 and so his score is 10 standard deviations below the mean.

The probability that a randomly selected student scored between 500 and 600 is about 0.34.

Lawmakers in a certain state surveyed 50 randomly selected registered voters in the state to see if they favor stricter laws regarding motorcycle helmet use for riders over the age of 17. Suppose it it known that in the population the proportion in favor of changing the law is 84%. Which of the following statements about the Central Limit Theorem conditions is correct? -The sample size is not large enough. -The population size is not large enough relative to the sample size. -The sample is not random. -All the conditions of the CLT are met.

The sample size is not large enough.

Which of the following statements is correct? - It is harder to reject a one-sided hypothesis test than a two-sided hypothesis test. -We will reject the null hypothesis only when the p-value is greater than the significance level. -When the test statistic is close to 0, we have proved that the null hypothesis is true. -The significance level provides a rejection region for us to determine whether evidence is strong enough or not.

The significance level provides a rejection region for us to determine whether evidence is strong enough or not.

A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0​: p=0.6 and Ha​: p ​< 0.6 The p-value was found to be 0.0655. For a significance level of ​0.05, choose the correct conclusion regarding the null hypothesis. -There is insufficient evidence to reject the null hypothesis, the population proportion is probably still equal to 0.6. -There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.6. -There is sufficient evidence to conclude that the population proportion is significantly less than 0.6. -There is insufficient data to determine the significance of the test.

There is insufficient evidence to reject the null hypothesis, the population proportion is probably still equal to 0.6.

A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The​ janitor's null hypothesis is that the supply of light bulbs has a defect rate of p=0.07 ​(the light bulb​ manufacturer's stated defect​ rate). Suppose he does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows H0​: p = 0.07 and Ha: p > 0.07 The janitor calculates a​ p-value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the​ p-value. -The​ p-value tells us that the true defect rate is approximately 0.087. -The​ p-value tells us that if the defect rate is​ 0.07, then the probability that we will observe am even more extreme test statistic is approximately 0.087. -The​ p-value tells us that the probability of concluding that the true defect rate is equal to​ 0.07 is approximately 0.087. -The​ p-value tells us that the probability of concluding that the true defect rate is great than 0.07 is approximately 0.087

The​ p-value tells us that if the defect rate is​ 0.07, then the probability that we will observe am even more extreme test statistic is approximately 0.087.

Suppose it is known that 23​% of students at a certain college participated in a textbook program each term. If a random sample of 500 students is​ selected, what proportion of the sample do we expect to participate in the textbook​ program? -We expect the sample proportion to be exactly 23​% because the sample size is large. -We expect the sample proportion to be exactly 23​% because that is the true proportion regardless of the sample or population size. -We do not expect the sample proportion to be exactly 23​% because it is a population parameter and you cannot know anything about a sample. -We expect that the sample proportion to be close to 23%​, but it will vary from sample to sample due to randomness.

We expect that the sample proportion to be close to 23%​, but it will vary from sample to sample due to randomness.

A fair coin is tossed 500 times. Which of the following statements shows correct understanding of the law of large numbers? -Since the probability of a tail is 0.5, you should expect exactly 250 tails in 500 tosses according the law of large numbers. -You may not get exactly 250 tails in 500 tosses, but the proportion of tails should be close to 0.5 as the number of tosses increases. -You should expect between 200 and 300 tails in 500 tosses. -You are less likely to get 250 tails than getting any other number of tails in 500 tosses.

You may not get exactly 250 tails in 500 tosses, but the proportion of tails should be close to 0.5 as the number of tosses increases.

Suppose that gas consumption (mpg) for trucks follows a normal distribution with a mean of 24 mpg and a standard deviation of 4 mpg. Which of the following statements is correct? -The top​ 2.5% trucks has gas consumption higher than 32 mpg. -The probability that the gas consumption of a randomly selected truck is higher than 40 mpg is close to 0. -The probability that a randomly selected truck has gas consumption between 20 mpg and 28 mpg is about 0.68. -All of the above.

all of the above