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.
Illinois  Ohio  Texas 
26.8  27.5  10.1 
17.6  28.9  18.8 
27  19.1  31.4 
20  36.9  44.2 
50.7  40.8  24.6 
24.4  9.5  29.5 
36.8  37.4  38.1 
42.2  38.9  30.3 
26.3  46.2  11.7 
14  35.8  35.8 
28.5  20.7  22.4 
36.9  37.8  17 
25.6  49.7  15.4 
25.9  44.3  15.4 
29.5  12.1  6.8 
29.7  43.7  14.8 
30.5  35.9  59.3 
20  30.2  5.3 
23.2  8.5  0.6 
20.7  34.6  20.7 
6.2  37.9  18.6 
44.2  50.9  24.9 
28.2  24.2  9.3 
28.8  39.1  11.9 
16.6  20.4  19.6 
20.2  12.4  31 
13.1  28  25.9 
16.9  28.4  52.6 
32.4  19.4  38.3 
19.6  42.5  34 
12.8  27.2  24.9 
30.2  22.6  32.1 
65.1  50.8  43 
25.5  34.1  31.1 
17.5  27.1  16.8 
11.1  38.9  34.1 
48.8  28.7  40.4 
38.9  54.2  29.4 
23.1  30.6  9.8 
21.6  15.9  19.5 
22.3  15.1  9.6 
27.3  30.1  21.6 
30.7  32.2  26.5 
In: Math
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 110 Likertscale from consumers utilizing the following attributes and corresponding levels,
Attribute  Level1  level 2  level 3  level 4 
Rasin Chewiness  low  medium  high  n/a 
Rasin Color  white  grey  brown  black 
Packaging Size  small  large  n/a  n/a 
Free Gift  no  yes  n/a  n/a 
Raisin Aroma  none  medium  heavy  n/a 
Price Compared to Market Leader  lower  same  higher  n/a 
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:
Regression Results from creating dummy variables
Coefficents  beta  std. error  tvalue  pvalue 
intercept  5.2991  0.3240  16.353  0.0000 
chew 1  0.8659  0.2437  3.5535  0.0006 
chew 2  0.3461  0.2438  1.4195  0.1593 
color 1  0.1211  0.2871  0.4218  0.6742 
color 2  0.2145  0.2802  0.7657  0.4459 
color 3  0.4799  0.2696  1.7801  0.0785 
Size large  0.8992  0.2000  4.4969  0.0000 
gift dummy  0.0916  0.2099  0.4365  0.6635 
aroma 1  0.5468  0.2563  2.1334  0.0357 
aroma 2  0.9715  0.2327  4.1742  0.0001 
Price 1  0.6548  0.2157  3.0362  0.0032 
Price 2  0.3237  0.2895  1.1180  0.2666 
Residual standard error: 0.9418 on 88 degrees of freedom
Multiple RSquared: 0.4276
Fstatistic: 5.976 on 11 and 88 degrees of freedom, the pvalue is 3.412e007
In: Math
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.
In: Math
Paired Samples ttest (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: Nondiet(subject 16): 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 16) : 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 tstatistic (2pts)
e) Compute the Pvalue (2pts)
f) At an alpha = 0.05 would you accept or reject the null hypothesis? (3pts)
Please show work, thank you!
In: Math
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.
In: Math
In: Math
Formulate both null and alternative hypotheses for the client, and explain why the hypotheses need to be directional or nondirectional.
Determine what statistical test should be used to analyze the data.
Summarize all information used to determine the correct statistical test (e.g., number of groups, type of data collected, independent or repeated measures)
Provide a sample size and critical values in relation to the hypothesis.
State what statistical test should be used (be specific since you have all of the information you need to determine the critical value(s)).
Discuss what the statistical analysis will do in answering the hypotheses and question(s) for the client. Also discuss any potential problems to watch out for, including an appropriate sample size to meet the assumptions of the statistical test.
Client Scenario: Jackson Hole Mind and Body Works
My name is Jane, and I am a licensed counselor who owns a business in Jackson Hole, Wyoming. This past year, I started a couple laughing yoga classes that combine the anxiety removing benefits of yoga with the emotional release of laughter. It has been a lot of fun and many clients love it, but a competitor has been criticizing my new approach as a sham and quackery. I am confident that my laughing yoga classes are beneficial, but I would like you to perform a study that examines the impact of my approaches from a scientific perspective. I know that science needs to be objective, so I would like you to setup a study for me as a nonbiased researcher. My thoughts are that I could give you the email addresses of clients who are willing to be in the study, and you would ask each of them questions, and then analyze the results.
I would like you to examine two types of therapy I conduct, my laughing yoga therapy and my more traditional cognitive behavioral therapy. I expect that 40 participants will be available from my laughing yoga classes, and that 50 participants will be available from my traditional cognitive behavioral therapy sessions. It would be nice if you asked questions related to clients’ current healthy living practices and use of positive emotions. You can determine the exact questions to ask clients. I was thinking that I would offer each participant in the study a couple free smoothie drinks at a local juice bar for participating in the research.
In: Math
Write an R function max.streak(p) that gives the length of the maximum "streak" of either all heads or all tails in 100 flips of a (possibly biased) coin whose probabilty of showing heads is pp.
Use your function to determine the expected length (rounded to the nearest integer) of the maximum streak seen in 100 flips of a coin when the probability of seeing "heads" is 0.700.70.
As a check of your work, note that the expected length of the maximum streak seen in 100 flips of a fair coin should be very close to 7.
In: Math
a. An experiment was performed on a certain
metal to determine if the strength is a function of heating time
(hours). Results based on 25 metal sheets are given below. Use the
simple linear regression model.
∑X = 50
∑X^{2} = 200
∑Y = 75
∑Y^{2} = 1600
∑XY = 400
Find the estimated y intercept and slope. Write the equation of the
least squares regression line and explain the coefficients.
Estimate Y when X is equal to 4 hours. Also determine the standard
error, the Mean Square Error, the coefficient of determination and
the coefficient of correlation. Check the relation between
correlation coefficient and Coefficient of Determination. Test the
significance of the slope.
b. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42inch plasma televisions (Consumer Report data slightly changed here):
Brand 
Price (X) 
Score (Y) 
Dell 
3800 
50 
Hisense 
2800 
45 
Hitachi 
2700 
35 
JVC 
3000 
40 
LG 
3500 
45 
Maxent 
2000 
28 
Panasonic 
4000 
57 
Phillips 
3200 
48 
Proview 
2000 
22 
Samsung 
3000 
30 
Use the above data to develop and estimated regression equation. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42inch plasma television with a price of $3600 and perform significance test for the slope.
In: Math
Number of People Making Contribution  
Ethnic Group  $150  $51100  $101150  $151200  Over $200  Row Total 
A  82  64  45  38  22  251 
B  91  54  67  30  22  264 
C  74  68  59  35  30  266 
D  98  87  71  54  30  340 
Column Total  345  273  242  157  104  1121 
(b) Find the value of the chisquare statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
In: Math
The population of Nevada, P(t), in millions of people, is a
function of t, the number of years since 2010. Explain the meaning
of the statement P(8) = 3. Use units and everyday language. (1
point)
2. Find the slopeintercept form of the equation of the line
through the points (8, 25) and (2, 13). (2 points)
3. At 8am, Charles leaves his house in Spartanburg, SC and drives
at an average speed of 65 miles per hour toward Orlando, FL. At
11:45am, he stops for lunch in Savannah, GA, which is 276.25 miles
from Orlando. a. Find a linear formula that represents Charles’
distance, D, in miles from Orlando as a function of t, time in
hours since 8am. (2 points)
b. Find and interpret the horizontal intercept. Remember to write
your intercept as a point! (2 points)
c. Find and interpret the vertical intercept. Remember to write
your intercept as a point! (2 points)
1
2
4. The temperature in ◦F of freshly prepared soup is given by T(t)
= 72 + 118e−0.018t, where t represents time in minutes since 6pm
when the soup was removed from the stove. a. Determine the value of
T(30) and interpret your answer in everyday language. (2
points)
b. Find and interpret the vertical intercept. Remember to write
your intercept as a point! (2 points)
5. Decide whether the following function is linear. Explain how you
know without ﬁnding the equation of the line.
x 9 12 16 23 34 f(x) 26.6 36.2 49 74.9 110.1
6. Attendance at a local fair can be modeled by A(t) = −30t2 + 309t
+ 20 people, where t represents the number of hours since 10am. a.
Find the average rate of change of the attendance from t = 3 to t =
8. Give units. (2 points)
b. Interpret your answer from (a) in everyday language.
In: Math
NO HANDWRITTEN ANSWERS PLEASE
The most common abuse of correlation in studies is to confuse the concepts of correlation with those of causation.
Good SAT scores do not cause good college grades, for example. Rather, there are other variables, such as good study habits and motivation, that contribute to both. Find an example of an article that confuses correlation and causation.
Discuss other variables that could contribute to the relationship between the variables.
In: Math
Bass  Samples: The bass in Clear Lake have weights that are normally distributed with a mean of 1.9 pounds and a standard deviation of 0.8 pounds.
(a) If you catch 3 random bass from Clear Lake, find the
probability that the mean weight is less than 1.0
pound. Round your answer to 4 decimal
places.
(b) If you catch 3 random bass from Clear Lake, find the
probability that the mean weight it is more than 3
pounds. Round your answer to 4 decimal
places.
In: Math
Why are sampling distributions important to the study of inferential statistics? In your answer, demonstrate your understanding by providing an example of a sampling distribution from an area such as business, sports, medicine, social science, or another area with which you are familiar. Remember to cite your resources and use your own words in your explanation.
In: Math
1) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?
Is the test statistic for this test Z or t?
Select one:
a. t
b. z
2) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?
What is the value of the test statistic of the test? ( Enter 0 if this value cannot be determined with the given information.)
3) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?
What is the pvalue of the test? (Enter 0 if this value cannot be determined with the given information.)
4) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?
What is the relevant bound of the rejection region? (Enter 0 if this value cannot be determined with the given information.)
5) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?
What decision should be made?
Select one:
a. Do not reject the null hypothesis
b. Can not be determined from given information
c. Accept the null hypothesis
d. Reject the null hypothesis
In: Math