indicate the term not synonymous with the others

How is the rejection region defined, and how is that related to the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?

Type “ineffective charts,” “ineffective graphs,” “unethical charts,” or some version thereof into Google Images. Find two or three differently-designed graphs and charts and discuss why the data visualizations are not effective.

Suppose your research assistant screwed up and lost the information that linked the person’s identity across the two weight loss periods. This makes it impossible to run a paired t-test. Rather than start over:

a) Compute the mean and standard deviation of the two samples (2-pts)

b) Compute the two sample t-statistic (2pts)

c) How many degrees of freedom do you have(3pts)?

d) compute the P-value (4pts)

e) How does this P-value compare to the one you just computed using the paired ttest? (3pts))

Two Sample t-test (16pts):

Suppose you are interested in deciding if the 1990 Toyota Four Runner has been equally reliable as the 1990 Honda Passport. You go out a randomly sample of 5 people who own a 1990 Toyota and 5 other people who own a 1990 Honda and you ask them how often they have to take their vehicles in for maintenance. Here are your data (in thousands of miles):

Toyota: 30 35 32 34 30

Honda: 29 33 28 31 27

a) State the null and alternative hypotheses (2pts)

b) Compute the means and standard deviations of the two samples (2-pts)

c) Compute the two sample t-statistic (2 pts)

c) How many degrees of freedom do you have? (3pts)

d) Compute the P-value (4pts)

e) At an alpha = 0.05 would you accept or reject the null hypothesis? (3pts)

Please show work! thank you!

8. A fair coin is tossed 60 times. Find the probability that the head appears between 22 and 40 times by using

a. binomial distribution,

b. approximation of Binomial distribution by normal distribution. Discuss why b. is better in practice.

ID      Year    CornYield       SoyBeanYield
1       1957    48.3    23.2
2       1958    52.8    24.2
3       1959    53.1    23.5
4       1960    54.7    23.5
5       1961    62.4    25.1
6       1962    64.7    24.2
7       1963    67.9    24.4
8       1964    62.9    22.8
9       1965    74.1    24.5
10      1966    73.1    25.4
11      1967    80.1    24.5
12      1968    79.5    26.7
13      1969    85.9    27.4
14      1970    72.4    26.7
15      1971    88.1    27.5
16      1972    97      27.8
17      1973    91.3    27.8
18      1974    71.9    23.7
19      1975    86.4    28.9
20      1976    88      26.1
21      1977    90.8    30.6
22      1978    101     29.4

23      1979    109.5   32.1
24      1980    91      26.5
25      1981    108.9   30.1
26      1982    113.2   31.5

27      1983    81.1    26.2
28      1984    106.7   28.1
29      1985    118     34.1
30      1986    119.4   33.3
31      1987    119.8   33.9
32      1988    84.6    27.0
33      1989    116.3   32.3
34      1990    118.5   34.1
35      1991    108.6   34.2
36      1992    131.5   37.6
37      1993    100.7   32.6
38      1994    138.6   41.4
39      1995    113.5   35.3
40      1996    127.1   37.6
41      1997    126.7   38.9
42      1998    134.4   38.9
43      1999    133.8   36.6
44      2000    136.9   38.1
45      2001    138.2   39.6
46      2002    129.3   38.0
47      2003    142.2   33.9
48      2004    160.3   42.2
49      2005    147.9   43.1
50      2006    149.1   42.9
51      2007    150.7   41.7

Use both predictors. From the previous two exercises, we conclude that year and soybean may be useful together in a model for predicting corn yield. Run this multiple regression.

a)       Explain the results of the ANOVA F test. Give the null and alternate hypothesis, test statistic with degrees of freedom, and p-value. What do you conclude?

b)      What percent of the variation in corn yield in explained by these two variables? Compare it with the percent explained in the previous simple linear regression models.

c)       State the regression model. Why do the coefficients for year and soybean differ from those in the previous exercises?

d)      Summarize the significance test results for the regression coefficients for year and soybean yield.

e)      Give a 95% confidence interval for each of these coefficients.

f)        Plot the residual versus year and soybean yield. What do you conclude?

Complete the following by writing a response to three of the four following questions. For each question, your response should be 2 or more paragraphs.
Describe how you could use confidence intervalsto help make a decision in your current job, a past job, or life situation. Include a description of the decision, how the interval would impact the decision, and how data could ideally be collected to determine the interval.

Analyses of drinking water samples for 100 homes in each of two different sections of a city gave the following means and standard deviations of lead levels (in parts per million).

(a) Calculate the test statistic and its p-value to test for a difference in the two population means. (Use Section 1 − Section 2. Round your test statistic to two decimal places and your p-value to four decimal places.)

z =

p-value =

Use the p-value to evaluate the statistical significance of the results at the 5% level.

a. H0 is not rejected. There is sufficient evidence to indicate a difference in the mean lead levels for the two sections of the city.

b. H0 is rejected. There is sufficient evidence to indicate a difference in the mean lead levels for the two sections of the city.   

c. H0 is rejected. There is insufficient evidence to indicate a difference in the mean lead levels for the two sections of the city.

d. H0 is not rejected. There is insufficient evidence to indicate a difference in the mean lead levels for the two sections of the city.

(b) Calculate a 95% confidence interval to estimate the difference in the mean lead levels in parts per million for the two sections of the city. (Use Section 1 − Section 2. Round your answers to two decimal places.)

parts per million______ to________parts per million

(c) Suppose that the city environmental engineers will be concerned only if they detect a difference of more than 5 parts per million in the two sections of the city. Based on your confidence interval in part (b), is the statistical significance in part (a) of practical significance to the city engineers? Explain.

a. Since all of the probable values of μ1 − μ2 given by the interval are all less than −5, it is likely that the difference will be more than 5 ppm, and hence the statistical significance of the difference is of practical importance to the the engineers.

b. Since all of the probable values of μ1 − μ2 given by the interval are all greater than 5, it is likely that the difference will be more than 5 ppm, and hence the statistical significance of the difference is of practical importance to the the engineers.   

c. Since all of the probable values of μ1 − μ2 given by the interval are between −5 and 5, it is not likely that the difference will be more than 5 ppm, and hence the statistical significance of the difference is not of practical importance to the the engineers.

A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.

e.) For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.

f.) For a sample of size 35, find the probability that the sample mean is more than 241.

g.) Compare your answers in part c and f. Why is one smaller than the other?

Consider the results from a completely randomized design showing commuting times in three states. Use an appropriate Excel ANOVA tool, to test for any significant differences in commuting times between the three states. Use α = 0.05.

We are considering a launch of a new type of raisin into the packaged raisin market. To do so, we collected product ratings on a 1-10 Likert-scale from consumers utilizing the following attributes and corresponding levels,

Please base your answer to the following questions on this data. Note that each attribute is coded numerically. For instance, for Chewiness (Low =1, Medium =2, High =3) and similarly for the other attributes reading left to right in the table above.

For each of the attributes, we code the levels into multiple dummy variables to include in our regression. The variables we used are as follows:

Note that for each category, the number of variables is equal to the number of levels – 1.

For example, for chewiness, we only need 2 dummy variables to show 3 levels:

• Chew1 = 1 and Chew2 = 0 indicates level 1 of chewiness.
• Chew1 = 0 and Chew2 = 1 indicates level 2 of chewiness.
• If neither Chew1 or Chew2 are 1 that only leaves level 3 of chewiness.

Regression Results from creating dummy variables

Residual standard error: 0.9418 on 88 degrees of freedom

Multiple R-Squared: 0.4276

F-statistic: 5.976 on 11 and 88 degrees of freedom, the p-value is 3.412e-007

1. Write down the model that was estimated in the regression, with the name of the variables and their coefficients in the model.
2. What Likert rating score would you predict for a raisin product that has Low Chewiness, Grey Raisins, Large Package Size, Free Gift, Medium Aroma, and the Same Price as the Market Leader? You may round your answer to the nearest integer.
3. What product has the highest predicted rating score?
4. Would you necessarily introduce this product, the one from previous part, if you were the decision maker?  Why or why not?
5. Suppose that the predicted market share of product j is proportional to R_j; that is market share, where R_jis the predicted Likert rating of product j. What would the predicted market share be if the product described in part b were introduced into the market consisting of current products i, ii, iii? The market currently contains the following three products:
   1. High Chewiness, Grey Raisins, Small Package Size, No Free Gift, Medium Aroma, and Same Price as the Market Leader’s (Likert =6.81)
   2. Low Chewiness, Brown Raisins, Small Package Size, Free Gift, Medium Aroma, and Same Price as the Market Leader’s (Likert =6.30)
   3. Medium Chewiness, Black Raisins, Large Package Size, No Free Gift, No Aroma, and Lower Price than the Market Leader’s (Likert =7.05)
6. Do the product attributes (as a whole) provide significant predictive power for the rating scores? Justify your answer.
7. Which product attributes, if any, have no statistically significant explanatory power for rating scores? State clearly how you arrived at your answer.

3. Independent random samples of n1 = 16 and n2 = 13 observations were selected from two normal populations with equal variances. The sample means and variances are shown below: Population 1 Population 2 Sample size 16 13 Sample mean 34.6 32.2 Sample variance 4.0 4.84 a) Suppose you wish to test if there is difference between the population means with significance level of α = 0.05. State the null and alternative hypotheses that you use for the test. b) Find the value of the test statistic c) Find the value of the critical value d) Conduct the test and state your conclusions.

Paired Samples t-test (30pts) Suppose you are interested in deciding if a particular diet is effective in changing people’s weight. You decide to run a “within subject” experiment. You select 6 people and weight each of them. Two weeks, you weight them again. For each person you compute how much weight they lost over this period. This is what you find: Non-diet(subject 1-6): 0 7 3 2 -10 -1

You then put them on the diet and weigh them again after two weeks and compute how much they lost over this period. Diet

(subject 1-6) : 1 6 4 3 -8 2

a) State the null and alternative hypotheses (2pts)

b) Compute the mean and standard deviation of the difference distribution (4pts)

c) How many degrees of freedom do you have? (3pts)

d) Assume the Null Hypothesis is True and compute the t-statistic (2-pts)

e) Compute the P-value (2pts)

f) At an alpha = 0.05 would you accept or reject the null hypothesis? (3pts)

Please show work, thank you!

Describe the difference between a one tailed and a two tailed test. What is the difference between a z test and a t test, and how do you determine which one to use? Also, discuss when a two sample test would be used, and provide an example.