Stats 12: Final CCLE Quizes Latest Update (2024/2025) Rated A+

Stats 12: Final CCLE Quizes Latest Update (2024/2025) Rated A+ When stating the null and alternative hypotheses, the hypotheses are: Select one: a. Always about the parameter only b. Always about the statistic only c. Always about both the statistic and the parameter d. Sometimes about the statistic and sometimes about the parameter a. Always about the parameter only The probability of rejecting the null hypothesis when, in fact, the null hypothesis is true is called the Select one: a. significance level b. power of the test c. standard error d. p-value a. significance level 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 0.01. 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. Select one: a. The significance level of 0.01 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 0.01 is the z-statistic that we will use to compare the observed outcome to the null hypothesis. c. The significance level of 0.01 is the probability of concluding that the defect rate is equal to 0.09 when in fact it is greater than 0.09. d. The sig a. The significance level of 0.01 is the probability of concluding the defect rate is more than 0.09 when it is equal to 0.09. Suppose that a one-proportion z-test statistic for a study is calculated to be 2.45. Which of the following is the most appropriate interpretation of this statistic? Select one: a. The study results are statistically significant. b. The observed value of the sample proportion is 2.45 SDs away from the parameter value assumed by the null hypothesis. c. The observed value of the sample proportion is 2.45 times the parameter value assumed by the null hypothesis. d. The observed value of the sample proportion is 2.45 SDs above the parameter value assumed by the null hypothesis. d. The observed value of the sample proportion is 2.45 SDs above the parameter value assumed by the null hypothesis. A quality control manager thinks that there is a higher defective rate on the production line than the advertised value of p = 0.025. She does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.025 and Ha: p > 0.025. She calculates a p-value for the hypothesis test of defective light bulbs to be approximately 0.067. Choose the correct interpretation for the p-value. Select one: a. The p-value tells us that the result is significantly higher than the advertised value using a significance level of 0.05. b. The p-value tells us that the probability of concluding that the defect rate is equal to 0.025, when in fact it is greater than 0.025, is approximately 0.067. c. The p-value tells us that the true population rate of defective light bulbs is approximately 0.067. d. The p-value tells us that if the defect rate is 0.025, then the probability d. The p-value tells us that if the defect rate is 0.025, then the probability that she would observe the percentage she actually observed or higher is 0.067. At a significance level of 0.05, this would not be an unusual outcome. 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. Select one: a. There is not sufficient evidence to reject the null hypothesis that the population proportion is equal to 0.4. b. There is not sufficient evidence to conclude that the population proportion is significantly less than 0.4. c. There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.4. d. There is sufficient evidence to conclude that the population proportion is significantly less than 0.4. d. There is sufficient evidence to conclude that the population proportion is significantly less than 0.4. 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. Select one: 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. H0: p = 0.16; Ha: p ≠ 0.16 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. Select one: a. No, the researcher did not collect a random sample. b. No, the population of interest is not large enough to assume independence. c. No, the researcher did not collect a large enough sample. d. Yes, all the conditions are satisfied. d. Yes, all the conditions are satisfied. 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. Select one: 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 for a two-sided test is divided by 2 resulting in a value less t d. 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 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? Select one: a. No error was made b. Type II error c. Type I error c. Type I error Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. Suppose we were to make a histogram of the feature length movie times of all movies in the past year. The histogram would be a display of which of the following? Select one: a. population distribution b. distribution of a sample c. Normal distribution d. sampling distribution of means a. population distribution Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. Suppose the process of taking random samples of size 20 is repeated 200 times and a histogram of the 200 sample means is created. The histogram would be a display of which of the following? Select one: a. distribution of a sample b. population distribution c. Normal distribution d. sampling distribution of means d. sampling distribution of means Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. What is the standard error for the mean feature length movie time of the 20 randomly selected movies? Round to the nearest thousandth. (Hint: In this scenario, is the population standard deviation known?) Select one: a. 0.356 b. 0.034 c. 0.055 d. 0.040 b. 0.034 Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. If we create a sampling distribution of sample means, what would be the mean and standard deviation of that distribution given the sample size of 20? Select one: a. The mean length would be 1.72 hours with a standard deviation of 0.18 hours. b. The mean length would be 1.80 hours with a standard deviation of 0.034 hours. c. The mean length would be 1.80 hours with a standard deviation of 0.18 hours. d. The mean length would be 1.80 hours with a standard deviation of 0.15 hours. b. The mean length would be 1.80 hours with a standard deviation of 0.034 hours. Choose the statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean. Select one: a. On average, the sample mean is the same as the population mean. b. The sample mean will always equal the population mean. c. We cannot say that the sample mean is unbiased. d. The standard deviation of the sampling distribution (also called the standard error) and the population standard deviation are equal. a. On average, the sample mean is the same as the population mean. 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? Select one: 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 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 25 is satis 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. 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. If a 95% confidence interval for the mean for the wedding sample is ($23465, $24983), does this mean that the sample results are significantly different from the claimed value for the mean of $25,200? Select one: a. Since the claimed population mean is outside of the 95% confidence interval, we conclude that there is a 95% chance that the sample results are significantly different. b. Since the accepted population average is outside of the 95% confidence interval, we conclude that the sample results are not significantly different. c. Since the claimed pop c. Since the claimed population mean is outside of the 95% confidence interval, we conclude that the sample results are significantly different. Suppose a consumer product researcher wanted to find out whether a Sharpie lasted longer than the manufacturer's claim that their Sharpies could write continuously for a mean of 14 hours. The researcher tested a random sample of 40 Sharpies and recorded the number of continuous hours each Sharpie wrote before drying up. Test the hypothesis that Sharpies can write for more than a mean of 14 continuous hours. Following are the summary statistics: bar(x) = 14.5 hours, s = 1.2 hours. At the 5% significance level, t = 2.635; p = 0.006. State your conclusion about the original claim. Select one: a. Reject the null hypothesis; there is strong evidence to suggest that the Sharpies last longer than a mean of 14 hours. b. There needs to be more data to determine if the Sharpies last longer than a mean of 14 hours. c. Reject the alternative hypothesis; there is strong evidence to suggest that the Sharpies last longer than a. Reject the null hypothesis; there is strong evidence to suggest that the Sharpies last longer than a mean of 14 hours. The weight of King Salmon from Lake Michigan and Lake Superior are measured. Researchers want to know whether Lake Michigan King Salmon weigh less than those from Lake Superior. The samples Select one: a. are dependent b. are independent b. are independent The productivity of manufacturing plant workers is compared before and after the installation of air conditioning. The samples Select one: a. are independent b. are dependent b. are dependent