Quiz 7

Samuel Morse suggested in the nineteenth century that the letter "t" made up 9% of the English language. Assume this is still correct. A random sample of 1000 letters is taken from a randomly selected, large book and the t's are counted. Find the approximate probability that the random sample of 1000 letters will contain 8.1% or fewer t's. a. about 16% b. about 32% c. about 5%

a

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Suppose an incoming legitimate message is flagged by the spam filter and sent to the spam folder. What type of error did the spam filter make? a. Type I error b. Type II error c. No error was made

a

Complete the statement by filling in the blanks: When constructing a confidence interval, if the level of confidence increases, the margin of error must _____ and the confidence interval will be _____. a. Increase; narrower b. Increase; wider c. Decrease; wider d. Decrease; narrower

b

The probability of rejecting the null hypothesis when, in fact, the null hypothesis is true is called the a. significance level b. Standard error c. p-value

a

When stating the null and alternative hypotheses, the hypotheses are: a. Always about the parameter only b. Sometimes about the statistic and sometimes about the parameter c. Always about both the statistic and the parameter d. Always about the statistic only

a

A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. State the hypotheses to be tested for this study. a. H0: p = 0.16; Ha: p > 0.16 b. H0: p = 0.16; Ha: p ≠ 0.16 c. H0: p = 0.16; Ha: p < 0.16 d. H0: p ≠ 0.16; Ha: p < 0.16

b

Choose the statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean. a. The standard deviation of the sampling distribution (also called the standard error) and the population standard deviation are equal. b. The sample mean will always equal the population mean. c. On average, the sample mean is the same as the population mean. d. We cannot say that the sample mean is unbiased.

c

A janitor at a large office building believes that his supply of light bulbs has a defect rate that is higher than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a manufacturer's defect rate of p = 0.09. He performs a test at a significance level of 0.05. The null and alternative hypothesis are as follows: H0 : p = 0.09 and Ha : p > 0.09. Choose the statement that best describes the significance level in the context of the hypothesis test. a. The significance level of 0.05 is the probability of concluding the defect rate is more than 0.09 when it is equal to 0.09. b. The significance level of 0.05 is the probability of concluding that the defect rate is equal to 0.09 when in fact it is greater than 0.09. c. The significance level of 0.05 is the z-statistic that we will use to compare the observed outcome to the null hypothesis. d. The significance level of 0.05 is the defect rate we believe is the true defect rate.

a

A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0 : p = 0.4 and Ha : p < 0.4 . The test statistic and p-value for the test are z = −3.01 and p−value = 0.0013 . For a significance level of α = 0.05 , choose the correct conclusion regarding the null hypothesis. a. There is sufficient evidence to conclude that the population proportion is significantly less than 0.4. b. There is not sufficient evidence to reject the null hypothesis that the population proportion is equal to 0.4. c. There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.4. d. There is not sufficient evidence to conclude that the population proportion is significantly less than 0.4.

a

A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. 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. a. No, the researcher did not collect a random sample. b. No, the population of interest is not large enough. c. Yes, all the conditions are satisfied. d. No, the researcher did not collect a large enough sample.

c

Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to a statistics study in the U.S., the average cost of a wedding in the U.S. in 2014 was $25,200. Recently, in a random sample of 35 weddings in the U.S. it was found that the average cost of a wedding was $24,224 with a standard deviation of $2,210. For this description, which of the following does NOT describe a required condition for a valid confidence interval based on the sample results? a. The sample distribution must be normally distributed in order to have a valid confidence interval. The problem does not describe the distribution of the sample, so this condition is not met. b. The sample observations are independent because knowledge about the cost of any one wedding tells us nothing about the cost of any other wedding in the sample. c. The description states that the sample was randomly selected, so we can assume that the condition which states that the data must represent a random sample is satisfied. d. The sample size of 35 is large enough that knowledge about the population distribution is not necessary and the condition that the population be normally distributed or sample size be larger than 30 is satisfied.

a

A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. A researcher completes a hypothesis test with a resulting p-value = 0.076. Choose the best statement to interpret the results. a. The standard cutoff value of α = 0.05 is multiplied by two for a two-sided test and the resulting value of 0.10 is greater than the p-value. Therefore there is no evidence to support that the city of interest has a different proportion of smokers than the general public. b. The p-value is above a standard cutoff value of α = 0.05 and therefore there is insufficient evidence to support that the city of interest has a different proportion of smokers than the general public. c. The p-value is above a standard cutoff value of α = 0.05 and therefore there is sufficient evidence to support that the city of interest has a different proportion of smokers than the general public. d. The p-value for a two-sided test is divided by 2 resulting in a value less than a standard cutoff value of α = 0.05 supporting the hypothesis that the city of interest has a different proportion of smokers than the general public.

b

A survey conducted five years ago by the health center at a university showed that 18% of the students smoked at the time. This year a new survey was conducted on a random sample of 200 students from this university, and it was found that 50 of them smoke. We want to find if these data provide convincing evidence to suggest that the percentage of students who smoke has changed over the last five years. What are the test statistic (Z) and p-value of the test? a. Z=2.58, p-value=0.0049 b. Z=2.29, p-value=0.0220 c. Z=2.29, p-value=0.0110 d. Z=2.58, p-value=0.0098

d

From a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for at least a week. An approximate 95% confidence interval is (0.50, 0.66). Which of the following statements is a correct interpretation? a. We are 95% confident that between 50% and 66% of the samples will have a proportion near 58%. b. 95% of the coworkers fall in the interval (0.50, 0.66). c. There is a 95% chance that a random selected coworker has gone on a vacation last year away from home for at least a week. d. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.

d