Flashcards
Unit 12 - One Sample Means Inference Test
Cards in this deck (25)
- 1The distribution of mass for United States pennies minted since 1982 is approximately normal with mean 2.5 grams. A random sample of 10 pennies minted since 1982 was selected. The sample had a mean mass of 2.47 grams and a standard deviation of 0.04 gram. The test statistic for the population mean has which of the following distributions?A t -distribution with 9 degrees of freedom
When the sample standard deviation is used instead of the population standard deviation, the test statistic follows a t-distribution with degrees of freedom equal to the sample size minus 1. In this case, the sample size was 10, so there are 9 degrees of freedom. - 2A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses H0 : μ = 12 versus Ha : μ < 12 was conducted, where μ represents the population mean number of ounces of the beverage dispensed per bottle by the machine. The p-value for the test was 0.05. Which of the following is the most appropriate conclusion to draw at the significance level of α = 0.10?Because the p-value is less than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.
- 3A fast-food restaurant claims that a small order of french fries contains 120 calories. A nutritionist is concerned that the true average calorie count is higher than that. The nutritionist randomly selects 35 small orders of french fries and determines their calories. The resulting sample mean is 135.2 calories, with a standard deviation of 32 calories. Which of the following is the approximate p-value for the appropriate test?0.0041
- 4A large city newspaper periodically reports the mean cost of dinner for two people at restaurants in the city. The newspaper staff will collect data from a random sample of restaurants in the city and estimate the mean price using a 90 percent confidence interval. In past years, the standard deviation has always been very close to $35. Assuming that the population standard deviation is $35, which of the following is the minimum sample size needed to obtain a margin of error of no more than $5 ?133
- 5There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 120 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?Approximately normal with mean $206,274 and standard deviation $3,458
- 6A century ago, the average height of adult women in the United States was claimed to be 63 inches. Researchers believe that the average might be greater today. A random sample of 40 adult women was selected from the population and a 95 percent confidence interval was constructed and given as 64.2 ± 0.927. Based on the interval, is the claim of 63 inches plausible?The claim is not plausible because 63 inches is not contained within the interval.
- 7A university researcher wants to estimate the mean number of novels that seniors read during their time in college. An exit survey was conducted with a random sample of 9 seniors. The sample mean was 7 novels with standard deviation 2.29 novels. Assuming that all conditions for conducting inference have been met, which of the following is a 95 percent confidence interval for the population mean number of novels read by all seniors?The point estimate is 7. The standard error is the sample standard deviation 2.29 divided by the square root of the sample size 9. There are n−1=9−1=8 degrees of freedom, and the correct value of t is 2.306.
- 8Porcupines can cause damage to wood structures by chewing them. Researchers studied a liquid repellent designed to reduce such damage. A sample of 20 wooden blocks of the same size were treated with the repellent and left outside in an area where porcupines are known to live. After a certain amount of time, the blocks were inspected for the number of porcupine teeth marks visible. The data were used to create the 95 percent confidence interval (4.9,5.8). Which of the following claims is supported by the interval?The mean number of porcupine teeth marks on all wooden blocks treated with the repellent is less than 6.
All plausible values for the population mean, 4.9 to 5.8, are less than 6. - 9A random sample of 10 employees of a company was selected to estimate the mean one-way commute time for all employees at the company. The mean and standard deviation of the sample were 38 minutes and 6 minutes, respectively. Assuming all conditions for inference are met, which of the following is the margin of error, in minutes, for a 99 percent confidence interval for the population mean one-way commute time?6.166
- 10A manufacturer of piston rings for automobile engines frequently tests the width of the rings for quality control. Last week, a random sample of 15 rings were measured, and the mean and standard deviation of the sample were used to construct a 95 percent confidence interval for the population mean width of the rings. When all other things remain the same, which of the following conditions would have resulted in a wider interval than the one constructed? I. A sample size of 20 with 95 percent confidence II. A sample size of 15 with 99 percent confidence III. A sample size of 12 with 95 percent confidenceII and III
Both statements II and III give conditions that increase the width of the interval. With all else remaining the same, the width of a confidence interval increases if sample size decreases or if confidence level increases. - 11The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams, while the standard deviation is 21 milligrams. What is the approximate test statistic for the appropriate test?-2.271
- 12Researchers are investigating the leg-strength of cyclers. They sample 70 cyclers and measure their leg strength. Peak power during cycling will be recorded for each cycler and the sample mean calculated. The sample mean was used to construct a 98 percent confidence interval for the population leg-strength of cyclers. Upon further discussion, the researchers decide that they want to decrease their margin of error by half. Which of the following is the best way to do this?Increase their sample size to 280.
- 13A large company is considering opening a franchise in St. Louis and wants to estimate the mean household income for the area using a simple random sample of households. Based on information from a pilot study, the company assumes that the standard deviation of household incomes is σ = $5,000. Of the following, which is the least number of households that should be surveyed to obtain an estimate that is within $150 of the true mean household income with 90 percent confidence?3100
- 14A century ago, the average height of adult women in the United States was 63 inches. Researchers believe that the average might be greater today. A random sample of 40 adult women was selected from the population. The sample had mean 64.2 inches and standard deviation 2.9 inches. Assuming all conditions for inference are met, which of the following is the appropriate alternative hypothesis that address their belief?Ha: µ > 63
- 15For which of the following is the shape of the sampling distribution of the sample mean approximately normal? I. A random sample of size 5 from a population that is approximately normal II. A random sample of size 10 from a population that is strongly skewed to the right III. A random sample of size 60 from a population that is strongly skewed to the leftI and III only
If the population is normal, the sampling distribution is assumed normal for any size sample, as is described in choice I. If the population is not normal, the sampling distribution is assumed normal if the size of the sample is at least 30, as is described in choice III. In choice II, the sample size is not large enough to assume a normal sampling distribution from a skewed population. - 16Most dermatologists recommend that the ideal shower lasts approximately 10 minutes. A researcher suspects that the average shower length of high school students is greater than 10 minutes. To test the belief, the researcher surveyed 125 randomly selected high school students and found that their average shower length was 14.7 minutes. With all conditions for inference met, a hypothesis test was conducted at the significance level of α=0.05, and the test produced a p-value of 0.0000. Which of the following is an appropriate conclusion?The researcher has statistical evidence to conclude that the population mean shower length for high school students is greater than 10 minutes.
The p-value of 0.0000 is less than the significance level of 0.05, and the correct decision is to reject the null hypothesis. There is statistical evidence to support the alternative hypothesis and conclude that the population mean shower length for high school students is greater than 10 minutes. - 17A researcher has conducted a two tailed hypothesis test on a population mean. Using a sample size of n = 310, he calculated a p-value of 0.0678. Which of the following must be true?A 95% confidence interval calculated from these data will include the researcher's hypothesized value.
- 18Which of the following statements correctly explains what happens to the variability of a t-distribution as the sample size increases?The variability of the t -distribution decreases as the sample size increases because the sample standard deviation approaches the population standard deviation.
As sample size increases, s approaches σ, and the t-distribution approaches the z-distribution. There are more observations closer to the center of a z-distribution than in any t-distribution, so the variability in a t-distribution decreases as the sample size increases because the t-distribution approaches a z-distribution. - 19For which of the following sample sizes would it be appropriate to create a normal probability plot in order to test for normalcy in a given sample if the population standard deviation is unknown? I. n = 9 II. n = 12 III. n = 25 IV. n = 100I, II, and III
- 20Given that all of the following are right tailed tests, which of the following calculated values of a test statistic would have the smallest p-value?z = 3.03
- 21A random sample of 50 students at a large high school resulted in a 95 percent confidence interval for the mean number of hours of sleep per day of (6.73, 7.67). When all other things remain the same, which of the following statements about the width of the interval is correct?The interval will be wider if 35 students are used in the sample.
- 22A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 12 seconds?0.0885
- 23Animal scientists studied foraging behavior of the scrub lizard, found in central Florida. Foraging is the process of searching for food. To study such behavior, the scientists recorded the number of head movements per minute for a sample of 63 lizards. A 95 percent confidence interval constructed from the sample is given as (2.08, 3.32) head movements per minute. Which of the following is an appropriate conclusion for the calculated interval?We are 95 percent confidence that the true mean number of head movements per minute for the scrub lizard is between 2.08 and 3.32 head movements per minute.
- 24A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127.95. and a standard deviation of $24.03. If the size of this sample is 40, which of the following is an approximate 95 percent confidence interval for the average cost of a repair at this repair shop?(120.26, 135.64)
- 25Which of the following correctly compares the t-distribution and z-distribution?The density curve of the t -distribution is more spread out than the density curve of the z -distribution, especially for small sample sizes.
The t-curve tends to be lower and wider than the z-curve, especially when the sample size is small.
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- 10th grade Math Flashcards on Unit 12 - One Sample Means Inference Test, created by Kelly Chen on 02/05/2021.
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