Question (statistics) (Data below) (to be done with EVIEWS or any data processor)

Millions of investors buy mutual funds, choosing from thousands of possibilities. Some funds can be purchased directly from banks or other financial institutions (direct) whereas others must be purchased through brokers (broker), who charge a fee for this service. A group of researchers randomly sampled 50 annual returns from mutual funds that can be acquired directly and 50 from mutual funds that are bought through brokers and recorded their net annual returns (NAR, %), which are the returns on investment after deducting all relevant fees.1 These data are saved in the two columns of the a1.xlsx spreadsheet labelled as Purchase and NAR, respectively. Import these data to EViews.

(a) Are Purchase and NAR qualitative or quantitative variables? If they are qualitative, are they ranked or unranked? If they are quantitative, are they discrete or continuous? What are their levels of measurement? Explain your answers.

(b) Use EViews to obtain the basic descriptive statistics for NAR. Briefly describe what they tell you about the net annual returns from mutual funds.

(c) Using the relevant statistics from part (b), estimate with 90% confidence the mean net annual returns. What assumption do you have to make to perform this task?

(d) Using the relevant statistics from part (b), briefly evaluate whether the assumption needed for the confidence interval in (c) is likely violated.

(e) In general, we can conduct hypothesis tests on a population central location with EViews by performing the (one sample) t-test, the sign test or the Wilcoxon signed ranks test.2 Suppose we would like to know whether there is evidence at the 5% level of significance that the population central location of NAR is larger than 5%. Depending on your answer in part (d), which test(s) offered by EViews would be the most appropriate this time? Explain your answer by considering the conditions required by these tests.

(f) Perform the test you selected in part (e) above with EViews. Do not forget to specify the null and alternative hypotheses, to identify the test statistic, to make a statistical decision based on the p-value, and to draw an appropriate conclusion. If the test relies on normal approximation, also discuss whether this approximation is reasonable this time.

(g) Perform the other tests mentioned in part (e). Again, do not forget to specify the null and alternative hypotheses, to identify the test statistics, to make statistical decisions based on the p-values, and to draw appropriate conclusions. Also, if the tests rely on normal approximation, discuss whether these approximations are reasonable this time.

(h) Compare your answers in parts (f) and (g) to each other. Does it matter in this case whether the population of net returns is normally, or at least symmetrically distributed or not? Explain your answer.

Data

A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80 . Suppose also that exactly 10% of the scores exceed 750 . Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place 7. suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of 0.2 inches and a standard deviation of 0.05 inches. What proportion of woodlice have antenna lengths that are less than 0.15 inches? Round your answer to at least four decimal places. 8. In a certain city of several million people, 6.8% of the adults are unemployed. If a random sample of 240 adults in this city is selected, approximate the probability that at most 14 in the sample are unemployed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.)

In certain drug trial, 10 subjects who received a placebo reported headaches, while 30 subjects who received a placebo reported no headaches. Of the subjects taking a new drug, 20 reported headaches, while 30 did not. a) Display this information in a contingency table, including all totals. b) What percentage of participants in the trial reported headaches? c) What percentage of new-drug takers reported headaches? d) What percentage of placebo takers reported headaches?

a) Draw a diagram to show a standard Normal distribution and shade in the regions between (µ–3(sigma)) and (µ+(sigma)). Find the approximate percentage of the population that would have values in this region. b) A researcher has found that among many mice in given maze the average time to complete the circuit is 10 minutes. The times were normally distributed with a standard deviation of 3 minutes. Find: i) the approximate proportion of mice that completed the maze in less than 4 minutes, ii) the probability that a random mouse takes more than 15 minutes to complete the maze, iii) the time to complete the maze below which are the fastest 5% of mice, and iv) the first quartile of the times to complete the maze

Use the following stem-and-leaf display of the ages of 10 persons.

1 | 2 4 4

2| 1 1 2 6 9

3| 2

4|

5 | 8

a) Find the mean and mode of the ages. b) By hand, find the five-number summary of the ages. c) Find the range and interquartile range of the ages. d) Provide a dot plot of the ages.

A shoe salesman wants to see if his female customers have a preference in the color of shoe purchased. He notes the color preferences of 100 randomly selected customers. The results: Black=32, Brown=27, Red=15, Navy =13 White =13

• Consider a t distribution with 7degrees of freedom. Compute

  P(t+≥ −1.05) Round your answer to at least three decimal places.

• Consider a t distribution with 11degrees of freedom. Find the value of c such that

  =P(-c < t < c)= 0.95 Round your answer to at least three decimal places.

• P(t≥ -1.05)=

• c=

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 131 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 262 days. From a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length. Find the 95% confidence interval to estimate the length of pregnancy for women who smoke. (Note: The critical z -value to use, z c , is: 1.960) ( , ) Your answer should be rounded to 3 decimal places.

Let X be the weight of a randomly selected 10oz bag of chips. Suppose that X has a normal distribution with a mean of 10.2 and standard deviation of .05. Find the weight of x* so that 95% of all 10oz bags have a weight of at least x*.

A coffee shop takes daily data on the high temperature for the day in degrees F, and the number of cups of hot chocolate sold. They construct a scatterplot and examine the linear relationship.The least squares regression line equation is:
y=76.42-1.38x

(1)Using the slope value, describe the relationship in context.

(2)Can this line equation be used to make a prediction for number of cups of hot chocolate sold when it's 60 degrees F outside? Explain.

A group of physicians were interested in understanding more about how much exercise their patients get each week. They randomly selected patients from their practice and asked each patient how much they exercise each week, in hours. With 95% confidence, they estimated that their patients exercise on average 3.1 hours per week with a margin of error of 1.4.

Why do you thin it was important for the physicians to randomly select patients to include in their sample? How would this be different if they took a convenience sample?

We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data481.dat) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.

(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

(c) State carefully what the slope tells you about the relationship between wages and length of service.

(d) Give a 95% confidence interval for the slope.
( _______ ,________ )

Answer all questions please

thank you

worker  wages   los     size
1       46.2755 117     Large
2       47.091  80      Small
3       47.8511 16      Small
4       59.5874 43      Small
5       38.4633 120     Large
6       71.1974 201     Small
7       38.8608 95      Large
8       50.6896 80      Large
9       56.9853 22      Large
10      45.4327 150     Small
11      58.0542 54      Large
12      55.6568 47      Small
13      54.9525 22      Small
14      55.8058 37      Large
15      53.6052 173     Large
16      60.9977 19      Large
17      49.5071 106     Large
18      55.4894 168     Small
19      45.1547 31      Large
20      51.0904 90      Large
21      82.706  53      Large
22      40.0094 85      Small
23      39.7198 78      Large
24      40.4793 130     Small
25      55.226  23      Large
26      67.7592 70      Small
27      37.2332 154     Small
28      62.0567 59      Large
29      48.24   54      Large
30      38.2374 57      Large
31      49.9539 75      Small
32      49.698  95      Large
33      42.1205 131     Large
34      65.2506 42      Small
35      43.5929 41      Large
36      40.8412 62      Large
37      44.0662 147     Large
38      79.6358 33      Small
39      37.1909 56      Large
40      37.3583 172     Small
41      52.1068 108     Small
42      41.5689 39      Small
43      59.9547 59      Large
44      46.6482 136     Small
45      55.733  73      Large
46      43.977  180     Small
47      37.4567 20      Large
48      40.3858 49      Large
49      43.2735 107     Small
50      49.7031 100     Large
51      43.4421 180     Large
52      50.0051 83      Large
53      48.7011 247     Large
54      55.1619 102     Small
55      45.6669 83      Small
56      53.5955 105     Large
57      39.6164 114     Small
58      67.3802 62      Large
59      60.3648 93      Small
60      65.0431 37      Large

As part of a disability services research project, an MPH student is analyzing data from a special survey conducted in Missouri. This survey was adapted from the Behavioral Risk Factor Surveillance System (BRFSS). The survey was a random digit dial telephone survey conducted in six Missouri counties between 2010 and 2012. The sample consisted of 3,343 adults: 1,380 from rural and 1,963 from nonrural areas. The survey collected information on residential information and the presence of a disability. Disability was defined as “activities are limited in any way because of an impairment or health problem.” The student hypothesized that disability would be increased in rural areas.

1. What kind of study is this and why?
2. What are the main concerns to make the causal inference based on the data from this study?

The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data5.dat gives the scores of 60 students who did this. How can we relate the two tests?

(a) Plot the data with SAT on the x axis and ACT on the y axis. Describe the overall pattern and any unusual observations.

(b) Find the least-squares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your P-value to four decimal places.)

(c) What is the correlation between the two tests? (Round your answer to three decimal places.)

obs     sat     act
1       950     17
2       719     19
3       648     17
4       905     22
5       1263    29
6       995     25
7       1184    25
8       672     13
9       882     17
10      1082    21
11      875     17
12      951     20
13      1045    22
14      679     19
15      794     18
16      722     16
17      1227    28
18      746     14
19      1145    27
20      716     19
21      1208    28
22      950     21
23      890     23
24      761     17
25      969     17
26      647     11
27      857     21
28      991     21
29      798     17
30      666     14
31      761     19
32      660     20
33      631     16
34      1121    26
35      978     26
36      883     18
37      807     18
38      895     19
39      1184    23
40      869     17
41      582     14
42      1070    20
43      642     16
44      937     23
45      1086    27
46      1013    26
47      713     19
48      1144    25
49      990     24
50      878     16
51      870     26
52      1090    27
53      1095    26
54      781     19
55      1046    21
56      675     13
57      1257    25
58      1099    27
59      620     10
60      714     13

explain how experimental design, analysis of variance, and chi square test are used in research.

A recent study of undergraduates looked at gender differences in dieting trends. There were 182 women and 109 men who participated in the survey. The table below summarizes whether a student tried a low-fat diet or not by gender:

(a) Fill in the missing cells of the table.

(b) Summarize the data numerically. What percent of each gender has tried low-fat diets? (Round your answers to two decimal places.)

(c) Test that there is no association between gender and the likelihood of trying a low-fat diet. (Round your χ² to three decimal places, and round your P-value to four decimal places.)

Summarize the results.

There is strong evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.There is no evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.