Statistics Homework help
Part 1: Please circle the correct answer.
1. Which of the following is most sensitive to outliers?
a. interquartile range b.standard deviation. c. median
d. mode
2. James and George took a math exam. George’s percentile score on the exam was 80; James’s
percentile score was 40 on the same test. We know that
a) George correctly answered twice as many questions than James. b) They both scored better than 40 of their classmates.
c) George correctly answered more questions than James. d) James did not pass the test.
3. Find the mean and standard deviation for a binomial experiment where n 260,
p 0.675 .
a) 260 , b) 260 ,
7.55
57.04
c) 175.50 ,
7.55
d) 97.50 ,
e) 175.50 ,
13.25
9.19
4. If we were to create a box plot, which of the following statement(s) would be true?
A. The median would be located somewhere within the box.
B. The median value would be larger than the third quartile value (Q3) C. The median would always be centered in the middle of the box.
D. The median would indicate where the 50th percentile would be.
a) A and B
b) All of them. c) A and D
d) C and D.
e) None of them.
5. Which of these statements are false?
a. There is a strong linear relationship between gender and height because we found a correlation of .55.
b. Plant height and leaf height were found to be negatively correlated because the correlation coefficient is -1.41.
c. Since the correlation between X and Y is 0, this means there is no relationship whatsoever between these two variables.
d. All of the above.
e. None of the above.
6. Some methods may be used to make a confidence interval wider or narrower. Circle the two
methods that would decrease the width of a confidence interval for a mean, if all else stays the same.
a. Increase the sample size. b. decrease the sample size.
c. increase the level of confidence. d. decrease the level of confidence.
7. Two researchers are going to take a sample of data from the same population of physics students. Researcher A will select a random sample of students from among all students taking physics. Researcher B’s sample will consist only of the students in her class. Both researchers will construct a 95% confidence interval for the mean score on the physics final exam using their own sample data. Which researcher’s method has a 95% chance of capturing the true mean of the population of all students taking physics?
a. Both methods have a 95% chance of capturing the true mean b. Researcher A
c. Research B
d. Neither
8. A 98% confidence interval indicates that:
a. 98% of the intervals constructed using this process based on samples from this population will include the population mean
b. 98% of the time the interval will include the sample mean
c. 98% of the possible population means will be included by the interval
9. A one-tailed hypothesis test is performed using a 0.10 level of significance. The P-value is determined to be 0.06. The null hypothesis
a. must be rejected
b. should not be rejected
c. both answers a and b could be correct, depending on the sample size d. has been designed incorrectly
10. A 95% confidence interval for a population mean is determined to be from 100 to 120. If the level of confidence is increased to 99%, the confidence interval for µ
a. becomes narrower
b. becomes wider
c. does not change d. becomes 0.1
11. If the sample size increases the standard error of the mean, a. increases.
b. decreases.
c. stays the same.
d. not enough information,
12. A car salesman calculates that he sells a car to 30% of the people to whom he discusses a potential sale. If on one day he talks to six unrelated customers about potentially buying a car, what is the probability that he will sell three cars on this day?
a. 0.082 b. 0.185 c. 1.111
d. 0.0492 e. 0.053
13. A Type I error is,
a. rejecting a false null hypothesis. b. rejecting a true hypothesis.
c. failing to reject a true null hypothesis. d. failing to reject a false hypothesis.
14. The dispersion (or variability) of the sampling distribution of sample means compare to the dispersion (or variability) of its corresponding population will be?
a. The sampling distribution would have more variability. b. The sampling distribution would have less variability. c. The variability would be the same.
d. The sampling distribution would have no variability.
15. If the slope of the regression (best fit) line is positive, then
a. y increases as x increases and the linear correlation coefficient will be positive.
b. y decreases as x increases and the linear correlation coefficient will be negative.
c. y does not change as x increases and the linear correlation coefficient will be zero. d. y does not change as x decreases and the linear correlation coefficient will be zero.
16. A researcher performs a hypothesis test at the 0.05 level of significance. The null hypothesis is p =
0.85and the alternative hypothesis is p is not equal to 0.85. The researcher calculates the sample
proportion to be 0.88 and the test statistic to be z* = 2.59 and the p-value to be 0.0096. Based on these results, the researcher correctly decides to reject the null hypothesis. Which statement correctly interprets the results of this hypothesis test.
a. The researcher has proven that the population proportion is 0.85.
b. The researcher has proven that the population proportion is different from 0.85. c. Evidence suggests that the population proportion is 0.85.
d. Evidence suggests that the population proportion is different from 0.85.
Part 2:
Question 1 and 2:
1. The following histogram shows the Verbal SAT scores for 205 students entering a local college in the fall of 2002.
A. How many of the students had verbal SAT scores between 425 and 724 inclusive?
B. How many students had verbal SAT scores less than 475 or greater than 674? If you can’t
determine that, please give a reason why.
C. How many students had verbal SAT scores below 400? If you can’t determine that, please
give a reason why.
3. The highway patrol in NY wants to know what percentage of motorists drive while wearing seatbelts.
A. Who should participate in this study? Please write your answer in complete sentences.
B. What type of visual display would be appropriate for displaying the data ? Explain why you choose that visual display in a complete sentence.
4. What is wrong with this statement? The correlation between the gender of a group of workers and the number of years they went to school was r = 0.10.
5a
b.
If we were to calculate the variance for each graph, which graph would show more variance? Please give a reason for your answer.
6. A sample of students were surveyed as to the number of hours they spent studying for their last Statistics test and the grade they received on the test. The data resulted in the following scatter diagram:
Statistics Test
95
90
85
80
Grade
75
70
65
60
0 1 2 3
4 5 6 7 8 9
Hours
6a. One student tells you that the linear correlation coefficient would be about -0.90. Is this student correct or incorrect? Please give a reason for your answer.
6b. Looking at the scatter plots, estimate the interval you think the linear correlation coefficient
would fall in.
(1) – 1.0 ≤ r < -0.5 (2) -0.5 ≤ r < 0 (3) 0 ≤ r < 0.5 (4) 0.5 ≤ r ≤ 1.0
7. Suppose you want to find out the grade you need to be in the top 20% of your class on an exam. From past experience your teacher estimates the mean will be 70 and the standard deviation will 10. What will be the minimum score needed to be in the top 20% of your class? Write your answer in a complete sentence.
8. If your histogram was J-shaped, in most cases would you use the mean or the median to represent the measure of central tendency? Give a reason for your answer in a complete sentence(s).
9. A researcher conducts a hypothesis test where he compares the scores of a random sample of students’ SAT scores to a national average (500). He hopes to show that the students’ mean score will be higher than average.
a. He finds a p-value for his sample of .03 and he used 0.05 as a level of significance. What decision should he make about accepting or rejecting the null hypothesis?
b. What is the chance that he makes an error? What type of error would this be?
10. Should you use a binomial distribution? Please give a reason for your answer. In a random sample of students “X” is the number of hours a person studies.
Part 3:
1. Women own on the average 25 pairs of shoes. This is based on a survey of female adults by Kelton Research for New York City – based Enslow, The Foot Comfort Center. Suppose a random sample of 30 female college graduate students is taken and the sample mean was
26.56 pairs of shoes with a sample standard deviation of 8.37. Does this sample provide sufficient evidence that the mean number of shoes for female graduate students is greater than the overall mean number for all female adults? Use a 0.05 level of significance.
a. State you decision and conclusion and explain how you reached your decision. Also please write down the formula you are using to find your test statistic. (10 points)
b. Find the 90% confidence interval to estimate the true mean umber of shoes for women based on this sample and write a confidence statement. (6 points)
2. Minitab :One-Sample Z: Weight (lb)
Test of mu = 36.5 vs < 36.5
The assumed standard deviation = 14.2
99% Upper
Variable N Mean StDev SE Mean Bound Z P Weight (lb) 64 32.11 14.30 1.77 36.24 -2.47 0.007
State your decision and conclusion using either the classical or p-value approach. (show how you arrived at your decision. (8 points)
Variable N Mean StDev SE Mean 92% CI T P
ages 30 25.397 3.895 0.711 (24.107, 26.688) 1.96 0.059
a. State you decision and conclusion using either the classical or p-value approach.(show how you arrived at you decision) ( 8 points)
b. Write your confidence statement for µ (the true mean population for ages). (6 points)
3. Test of mu = 24 vs not = 24
4. A recent survey of 300 randomly selected fourth graders showed that 210 participate in at least one organized sport during one calendar year. Construct a 95% confidence interval for the proportion of fourth graders who participate in an organized sport during the year and write a confidence statement. (10 points)
5. In a poll conducted by the American Association of Retired Persons of 1706 adults aged 45 and older, 72% agreed with the statement that, “adults should be allowed to legally use marijuana for medical purposes if a physician recommends it.” Suppose a recent study of 200 adults in the Midwest showed 130 in favor of legally using marijuana for medical purposes. Do these results show a lower proportion for the Midwest in respect to the rest of the country? Use a 0.05 level of significance. Please show how you reached your decision. (10 points)
Fitted Line Plot
6.
Weight = – 186.5 + 4.706 Height
140
130
120
Weight
110
100
S 10.1460
R-Sq 63.7% R-Sq(adj) 57.6%
90
60 61
62 63
64 65 66
67 68 69
Height
The above graph is displaying data for height and weight. a. What is the independent variable?(2 points)
b. What is the dependent variable?(2 points)
c. Write a sentence to interpret the y – intercept of the line. (4 points)
d. Write a sentence interpreting the slope of the line with regard to your graph. (4 points)
e. Using the equation for the line of best fit, estimate the weight of a person with a height of
62.5 inches. If you can’t estimate it, please give a reason why. (4 points)
f. Using the equation of the line of best fit, estimate the weight of a person who is 18 inches?
If you can’t estimate it, please give a reason why. (4 points)
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