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STA 2023 PARTIAL REVIEW FOR FINAL WITH KEY
- Find the median of the following set of numbers:
a. 5 b. 6 c. 7 d. 3
- In a test of hypothesis the test p-value is always compared to the:
a. test statistic b. level of significance c. sample mean d. critical value
- The test scores reported for a nationally administered college achievement test have a normal distribution with a mean of 520 and a standard deviation of 110. My score is 2 standard deviations below the mean. Which is a true statement:
a. Less than 5 % of those who took the test made a score higher than mine. b. Less than half of those who took the test made a score higher than mine. c. Less than 5 % of those who took the test made a score lower than mine. d. My score was in the top 5 % of those who took the test.
These are boxplots of the salaries made by employees of a company. 0 is for males and 1 is for females.
Which of the following is a true statement about the boxplots. a. The median salary for females is about the same as the median salary for males. b. There is more variation in the salaries for men. c. The median salary for women is less than the minimum salary for men. d. The salaries for the women as a whole are about the same as the salaries for the men as a whole.
0 1
40000
35000
30000
25000
GENDER N
SA LA RY
- A social researcher in a particular city wishes to obtain information on the number of children in households that receive welfare support. A random sample of 400 households was selected from the welfare rolls of the city. A check of welfare recipient data identified the number of children in each household. Identify the population that is of interest to the researcher.
a. all households in this particular city b. the children receiving welfare support in the 400 households that were selected c. 400 households receiving welfare support that were selected d. the households in this particular city that are listed on the welfare rolls of the city
- Consider the following two variables: X: number of hours per week that an adult exercises Y: number of days per year that the person misses work due to illness
The linear correlation coefficient between X and Y is equal to -.. Select the best interpretation of the correlation between X and Y.
a. The strength of the linear correlation between exercise and days missed due to illness is weak. The more a person exercises, the more days of work he misses due to illness.
b. The strength of the linear correlation between exercise and days missed due to illness is strong. The more a person exercises, the more days of work he misses due to illness.
c. The strength of the linear correlation between exercise and days missed due to illness is weak. The more a person exercises, the less days of work he misses due to illness.
d. The strength of the linear correlation between exercise and days missed due to illness is strong. The more a person exercises, the less days of work he misses due to illness.
- The following is the number of words typed in a 5 minute civil service test taken by 12 different applicants: 174 181 142 157 181 183 163 130 170 164 183 198
What is the 25th percentile of these numbers:
a. 130 b. 160 c. 172 d. 182
- When 500 college students are randomly selected and surveyed, it is found that 135 of them own personal computers. Find a 95 % confidence interval for the true proportion of all college students who own personal computers.
a. (.238, .302) b. (.269, .271) c. (-.03, .044) d. (.231, .309)
- The skid properties of a snow tire have been tested, and a mean skid distance of 154 feet has been established for standardized conditions. A new, more expensive tire is developed, but tests on a sample of 20 new tires yield a mean skid distance of 141 feet with a standard deviation of 12 feet. Because of the cost involved, the new tires will be purchased only if it can be shown at the α = .05 significance level that they skid less than the current tires. What would be the test statistic for the test of hypothesis?
a. -.242 b. -4.845 c. -1.083 d. -2.
- A sample of 93 IQ scores was randomly selected from a certain population. At a level of significance equal to .01 we want to test whether the population has a mean IQ score equal to 105 versus being different from 105. If we run the test on a computer and get a p-value of .015, what would be your conclusion?
a. We are 99% sure that the mean IQ is equal to 105. b. We are 99% sure that the mean IQ is not equal to 105. c. At a significance level of .01 there is not sufficient evidence to conclude that the mean is different from 105.. d. At a significance level of .01, we reject the null hypothesis and conclude that the mean is different from 105.
- Consider the following table for the number of cars owned by 20 randomly selected households: 1 2 3 4 1 2 3 1 2 3 1 2 1 2 1 2 2 2 2 2
The mean of this distribution is:
a. 1.95 b. 2.5 c. 5 d. 9.
- The median of the distribution in the preceding problem is:
a. 1 b. 1.5 c. 2 d. 2.
- What do you include when describing a scatterplot of two variable data: a. pattern and strength b. direction of the association c. outliers and influential observations d. all of the above
For the above histogram, which statement is true? a. The mean is approximately 250. b. The mean is less than the median. c. The range of the data is 250. d. The range of the data is 9.
0 1 2 3 4 5 6 7 8 9 10
200
100
0
C
Frequency
- For the following set of numbers where would the upper fence be that determines high outliers? 42 78 25 88 48 83 82 34 100 52 91 58 95 41 66 70 75 72 78 76
a. 82. b. 115 c. 131. d. 148.
- Find the Z value such that 15% of the standard normal curve is to the right of Z.
a. .5596 b. .7734 c. 1.03 d. –1.
- Consider the following two data sets and then circle the true answer.
Data set #1: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 Data set #2: 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7
a. The standard deviation of data set 1 is the same as the standard deviation of data set # b. The standard deviation of data set 1 is more than the standard deviation of data set # c. The standard deviation of data set 1 is less than the standard deviation of data set # d. It is impossible to know the relationship between the standard deviations of the two data sets without calculating the standard deviation of each.
- What is the correct conclusion if we do not reject the following null hypothesis?
H
Ha
0 0 0
μ μ
a. There is sufficient evidence to conclude that the mean is equal to 100. b. There is not sufficient evidence to conclude that the mean is less than 100. c. There is sufficient evidence to conclude that the mean is less than or equal to 100. d. There is sufficient evidence to conclude that the mean is less than 100.
- In an insurance company study of New York State licensed drivers' ages, 570 randomly selected ages have a mean of 41.8 years and a sample standard deviation of 16.7 years. What is a 90% confidence interval for the mean age of all New York State licensed drivers. a. (40.6, 43.0) b. (40.4, 43.2) c. (41.75, 41.85) d. (14.3, 69.3)
- Which of the following is affected the least by an outlier: a. correlation coefficient b. standard deviaton c. mean d. median
- Consider the following histogram.
57 59 61 63 65 67 69 71
15
10
5
0
HEIGHTS
Frequency
What percentage of this population has heights between 61 and under 65 inches? a. 21% b. 27% c. 36% d. 60%
- In a test of hypothesis the p value is .0001. Select the true statement: a. the proof of the alternate hypothesis is very weak because the p value is close to zero so the chances of being correct are close to zero. b. there is not enough evidence to reject the null hypothesis c. since the P-value is so small we need to obtain a larger sample and do a second test of hypothesis d. it is almost impossible to have gotten these results from the sample if the null hypothesis is true
