Quant II Midterm
A random sample of 200 households in Norman reveals that 20% have Internet access while a random sample of 250 households in Moore yields 38 who have Internet access. What is the 95% confidence interval for the difference in Internet access in the two communiites
G. HT Z Two Proportions
To determine whether a certain type of fertilizer is more effective than another, 200 plants are fertilized with type A and 300 are fertilized with type B fertilizer. 100 plants with type A demonstrate satisfactory growth while 180 plants with type B demonstrate satisfactory growth.
G. HT Z Two Proportions
The average level of prothrombin in a certain population of 50 individuals is 20 mg/100 ml of blood plasma with a standard deviation of 4 milligrams/100 ml. For another group, a sample is taken from 40 individuals in whom the average was 18.5 mg/100 and the standard deviation was 3.6 milligrams/100 ml. Can the variances be assumed to be equal?
H. HT F Var Ratio
In reference to the above, what would be the upper bound of a 90% confidence interval about the sample mean, approximately? A) 283 B) 341 C) 78.54 D) 168
A) 283
The statistical distribution used for testing the difference between two population variances is the ________ distribution. A) F B) standardized normal C) binomial D) t
A) F
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an mean of 257.3 W. Referring the above discussion, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are: A) H0 : μ ≤ 250 versus H1 : μ > 250 B) H0 : μ ≥ 257.3 versus H1 : μ < 257.3 C) H0 : μ > 250 versus H1 : μ ≠ 250 D) H0 : μ ≥ 250 versus H1 : μ < 250
A) H0 : μ ≤ 250 versus H1 : μ > 250
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision. Referring to the above discussion, the appropriate hypotheses are: A) H0 : μ ≥ 7.4 versus H1 : μ < 7.4 B) H0 : μ > 7.4 versus H1 : μ ≤ 7.4 C) H0 : μ ≤ 7.4 versus H1 : μ > 7.4 D) H0 : μ = 7.4 versus H1 : μ ≠ 7.4
A) H0 : μ ≥ 7.4 versus H1 : μ < 7.4
Suppose we want to test H0 : μ ≥ 30 versus H1 : μ < 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of H1? A) Xbar= 27, S = 4 B) Xbar = 28, S = 6 C) Xbar= 32, S = 2 D) Xbar= 26, S = 9
A) Xbar= 27, S = 4
Suppose a 95% confidence interval for μ has been constructed. If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would ________. (Assume that the sample statistics gathered would not change very much for the new sample.) A) be narrower than the current interval width B) be larger than the current interval width C) be unknown until actual sample sizes and reliability levels were determined D) be the same as the current interval width
A) be narrower than the current interval width
In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a A) narrower B) biased C) wider D) less significant
A) narrower
For sample size 1, the sampling distribution of the mean will be normally distributed A) only if the population is normally distributed. B) only if the shape of the population is symmetrical. C) regardless of the shape of the population. D) only if the population values are positive.
A) only if the population is normally distributed.
The life span of 100 W light bulbs manufactured by a particular company follows a normal distribution with a standard deviation of 120 hours and its life is guaranteed under warranty for a minimum of 800 hours. At random, a sample of 250 bulbs from a lot is selected and it is revealed that the life is 750 hours. With a significance level of 0.01, should the lot be rejected by not honoring the warranty?
A. HT Z Mean
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: Xbar= $50.50 and S2= 400. Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution. A) $50.50 ± $9.09 B) $50.50 ± $11.08 C) $50.50 ± $11.00 D) $50.50 ± $10.12
B) $50.50 ± $11.08
Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in 2009. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $3.5 million. A) 0.9772 B) 0.0228 C) Approximately 1 D) Approximately 0
B) 0.0228
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: Xbar=$50.50 and S2 = 400. What is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ? A) a standard normal distribution B) a t distribution with 14 degrees of freedom C) a t distribution with 15 degrees of freedom D) approximately normal with a mean of $50.50
B) a t distribution with 14 degrees of freedom
A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The decision on the hypothesis test using a 3% level of significance is A) We cannot tell what the decision should be from the information given. B) to reject H0 in favor of H1. C) to fail to reject H0 in favor of H1. D) to accept H0 in favor of H1.
B) to reject H0 in favor of H1.
A Type I error is committed when A) we reject a null hypothesis that is false. B) we reject a null hypothesis that is true. C) we don't reject a null hypothesis that is true. D) we don't reject a null hypothesis that is false.
B) we reject a null hypothesis that is true.
The quality control division of a factory that manufactures batteries suspects defects in the production of a model of mobile phone battery which results in a lower life for the product. Until now, the time duration in phone conversation for the battery was a mean of 300 minutes. However, in an inspection of the last batch produced before sending it to market, it was found that the average time spent in conversation was 290 minutes in a sample of 16 batteries with a standard deviation of 28 minutes. Can it be concluded that the quality control suspicions are true at a significance level of 1%?
B. HT t Mean
In reference to the above, what is the t-value that yields 5% in the left tail, approximately? A) -2.33 B) -1.96 C) -1.89 D) -1.64
C) -1.89
In reference to the above, what is the standard deviation, approximately? A) 196 B) 264 C) 143 D) 86
C) 143
A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence? A) 105 B) 420 C) 150 D) 597
C) 150
In reference to the above, what is the standard error of the mean, approximately? A) 86 B) 25 C) 50.6 D) 54
C) 50.6
Suppose the ages of students in Statistics 101 follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? A) The mean of the sampling distribution is equal to 23 years. B) The shape of the sampling distribution is approximately normal. C) The standard deviation of the sampling distribution is equal to 3 years. D) The standard error of the sampling distribution is equal to 0.3 years.
C) The standard deviation of the sampling distribution is equal to 3 years.
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled? A) n = 1,503 B) n = 1,435 C) n = 1,784 D) n = 1,844
C) n = 1,784
A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random, 300 peanuts were selected and 21 of them were empty.
C. HT Z Proportion
The proportion of individuals in a population with some form of color blindness is thought to be 20%. If the sample size is 160 individuals, and the percentage of color blind individuals in the sample is 25%, determine using a significance level of 1%, would the null hypothesis be rejected, based on this confidence interval?
C. HT Z Proportion
Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for the mean endowment of all private colleges in the United States? A) $1,447.8 B) $8 C) $143.042 D) $180.975
D) $180.975
Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in 2009. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million. A) Approximately 0 B) Approximately 1 C) 0.9849 D) 0.0151
D) 0.0151
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger? A) 0.4987 B) 0.0001 C) 0.0013 D) 0.0228
D) 0.0228
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 16 fish is taken, what would the standard error of the mean weight equal? A) 0.050 B) 0.800 C) 0.003 D) 0.200
D) 0.200
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. Because the population is normally distributed, so too will be the sample mean. What is the expectation of the percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds? A) 84% B) 16% C) 29% D) 60%
D) 60%
The t distribution A) has more area in the tails than does the normal distribution. B) assumes the population is normally distributed. C) approaches the normal distribution as the sample size increases. D) All of the above.
D) All of the above.
For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. A) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes. B) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes. C) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes. D) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.
D) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.
A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose you reject the null hypothesis. What conclusion can you draw? A) There is sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90. B) There is not sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90. C) There is not sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90. D) There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.
D) There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for π is 0.59 ± 0.07. Interpret this interval. A) We are 95% confident that 59% of the students are on some sort of financial aid. B) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid. C) 95% of the students get between 52% and 66% of their tuition paid for by financial aid. D) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.
D) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.
You know that the level of significance (α) of a test is 5%, you can tell that the probability of committing a Type II error (β) is A) 97.5%. B) 2.5%. C) 95%. D) unknown, Type II errors compuations required specification of the althernative hypothesis value.
D) unknown, Type II errors compuations required specification of the althernative hypothesis value.
Two production designs are tested for worker productivity. With the first design, in a sample of 20 workers, average output was 10 units with a standard deviation of 2. With a different set of 24 workers the average output was 12 with a standard deviation of 3. The variances for the two groups of workers are assumed to be equal. Do the experimental results imply that a statistically significant difference exists between the two production designs?
D. HT Pooled-Var t Mean
For sample size 64, the sampling distribution of the mean will be approximately normally distributed A) if the shape of the population is symmetrical. B) if the population is normally distributed. C) regardless of the shape of the population. D) if the population standard deviation is known. E) All of the above.
E) All of the above.
Training is provided to 36 workers to improve productivity in production. Before and after training data are collected for the workers and statistical tests are performed to see whether there is a significant improvement.
E. HT Diff mu Paired t
A sample of 50 males in a specific occupational category yields a mean monthly salary of $5000 with a standard deviation of $500 while a sample of 50 females in that same occupational category yields a mean monthly salary of $4800 with a sample standard deviation of $600. Under the assumption that the variances are not equal, is there evidence to reject the null hypothesis of no difference in monthly salary at the 0.05 level of significance versus an alternative hypothesis that they are not equal? What if the alternative hypothesis was that the male salary is greater than the female salary?
F. HT Diff mu Separate-Var t
It is hypothesized that the monthly earnings of house painters differs from that of carpenters. A sample of 24 house painters yields a mean of $4,000 with a a standard deviation of $200 while a sample of 26 carpenters yields a mean of $4,300 with a standard deviation of $300. Is there sufficient evidence to reject a null hypothesis of equality in earnings?
F. HT Diff mu Separate-Var t
T/F: A sample of 100 fuses from a very large shipment is found to have 10 that are defective. The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.
False
T/F: The mean of the sampling distribution of a sample proportion is the population proportion, π.
True
Suppose that a study of 200 adults (18 and older) found that 36 of them were smokers. The upper limit of the 90% confidence interval for the proportion of smokers is: a) 0.2148 b) 0.2247 c) 0.1353 d) 0.1452
b) 0.2247
Owing to increased enforcement on uninsured motorists, the Department of Motor Vehicles Department asserts that over a 3% reduction has occurred from previous rates of 16.1%. To test this assertion, the most appropriate alternative hypothesis is: a) H1: p > 13.1% b) H1: p< 16.1% c) H1: m <= 16.1 d) H1: p < 13.6
a) H1: p > 13.1%
A two-tail test is conducted with a sample size of 20. The value of the t statistic is -2.25. At the 1% level of significance, should the null hypothesis be rejected? a) No, because -2.25 lies within the 99% confidence interval (±2.861). b) No, because -2.25 lies within the 99% confidence interval (±2.539) c) No, because -2.25 lies within the 99% confidence interval (±2.849) d) No, because -2.25 lies within the 99% confidence interval (±2.528)
a) No, because -2.25 lies within the 99% confidence interval (±2.861).
If a hypothesis is rejected at the 5% level of significance: a) It must be rejected at the 10% level of significance. b) It may be rejected at the 10% level of significance. c) It will also be rejected at the 1% level of significance. d) Cannot be answered given the provided information.
a) The manufacturer's stated weight of 0.81oz is true.
What value of Z defines a 3% tail at the right-end of the distribution? a) -1.881 b) 1.881 c) 3 d) 2.17
b) 1.881
A personal financial manager claims that the expected return on the portfolios that he manages exceeds 16%. To test the claim about the expected return for his managed portfolios, the appropriate procedure to use is: a) A right-tail hypothesis test with H0: p<=16%, H1: p >16%. b) A left-tail hypothesis test with H0: p>=16%, H1: p <16%. c) A two-tail test of the average portfolio return. d) A two-tail test of the standard deviation of the portfolio returns.
b) A left-tail hypothesis test with H0: p>=16%, H1: p <16%.
A sampling distribution refers to: a) The probability distribution of a variable. b) A probability distribution of a sample statistic. c) The frequency distribution of a random variable. d) The distribution of all samples taken from a given population.
b) A probability distribution of a sample statistic.
Statistical Inference is best described as: a) Inferring that the statistics are accurate due to correct statistical procedures. b) Making true statistical statements about a sample population. c) Drawing of conclusions about a population of interest based on findings from samples obtained from that population. d) Using attributes such as the mean and standard deviation to make observational statements about data.
c) Drawing of conclusions about a population of interest based on findings from samples obtained from that population.
A sampling error is caused by: a) The use of nonrandom sampling. b) Sampling using the wrong approach (e.g., taking a cluster sample when a stratified sample was needed). c) The difference between the true population parameter and the estimated sample statistic. d) Errors that occur during either data transcription or data entry.
c) The difference between the true population parameter and the estimated sample statistic.
The critical value for testing hypotheses about a single population's proportion comes from: a) The normal distribution b) The binomial distribution c) The normal distribution, as long as the sample is sufficiently large d) It is calculated from the sample proportions.
c) The normal distribution, as long as the sample is sufficiently large
The p-value is: a) The probability of obtaining any value in the normal distribution. b) The probability of obtaining any Z value in the standard normal distribution. c) The probability of obtaining a Z value farther away from the mean than a specified Z value. d) The probability of obtaining a Z value closer to the mean than a specified Z value.
c) The probability of obtaining a Z value farther away from the mean than a specified Z value.
The central limit theorem states that: a) The sampling distribution of the mean is normal only when the sample is drawn from a normally distributed population. b) The sampling distribution of the mean is always normal with a mean of m and a standard deviation of m c) The sampling distribution of the sample mean drawn from any population is normal as long as the sample size is sufficiently large. d) The sampling distribution of the mean follows the same distribution as the population that the sample is drawn from.
c) The sampling distribution of the sample mean drawn from any population is normal as long as the sample size is sufficiently large.
The width of a confidence interval: a) Increases as the sample size increases. b) Decreases as the standard deviation increases. c) Increases as the sample mean increases. d) Increases as the confidence level increases.
d) Increases as the confidence level increases.
A two-tail test is conducted with a sample size of 25. The value of the t statistic is -1.68. At the 5% level of significance, should the null hypothesis be rejected? a) Yes, because -1.68 is smaller than the critical value of 1.711. b) Yes, because -1.68 is smaller than the critical value of 2.064. c) No, because -1.68 is not smaller than the critical value of -1.711. d) No, because -1.68 is not smaller than the critical value of -2.064.
d) No, because -1.68 is not smaller than the critical value of -2.064.
The sample size should be: a) Larger when the population displays high variability. b) Larger when the consequences of making a Type I or Type II error is high. c) Smaller when you are tolerant of sampling errors. d) Larger for proportions then for continuous variables e) All of the above.
e) All of the above.
A tennis player is trying to improve the consistency of her serves, her goal is that she hits less than 15 percent of her first serves out-of-bounds. In a weekend of practice she hits 400 serves and 50 of them are out-of-bounds: a) This is best seen as a left-tail test with H1: p< 15% b) This is best seen as a right-tail test because the question is whether she misses on more than 10 percent of serves c) This "goal" statement is seen as a minimal requirement, and therefore the question is whether actual sample results are suggestive that the true mean is less than 15%. d) There is insufficient information to conduct a test. e) Both a and c above.
e) Both a and c above.
A machine allocates miniature cookies to 100 calorie packages. According to the manufacturer, the average weight of the bag should be 0.81oz with a standard deviation of 0.03oz. The mean weight of a random sample of ten bags is taken and the mean weight is 0.82oz. In consequence: a) It is reasonable to assume that the machine is calibrated correctly. b) It is highly likely that the machine is in need of adjustment, c) Adjustment is probably not necessary because deviations more than one standard error of the mean are not uncommon in statistical analysis. d) Both a and c above. e) Cannot be determined given the provided information.
e) Cannot be determined given the provided information.
