9.3.3

A study was conducted that measured the total brain volume (TBV) (in ) of patients that had schizophrenia and patients that are considered normal.  Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients ("SOCR data oct2009," 2013).  Is there enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal?  Test at the 10% level.

Table #9.3.5: Total Brain Volume (in ) of Normal Patients

Table #9.3.6: Total Brain Volume (in ) of Schizophrenia Patients

A random sample of 100 observations from a population with standard deviation 22.99 yielded a sample mean of 94.1. 1. Given that the null hypothesis is μ≤90 and the alternative hypothesis is μ>90 using α=.05, find the following: (a) Test statistic = (b) P - value: (c) The decision for this test is: A. Fail to reject the null hypothesis B. Reject the null hypothesis C. None of the above 2. Given that the null hypothesis is μ=90 and the alternative hypothesis is μ≠90 using α=.05, find the following: (a) Test statistic = (b) P - value:

The sampling distribution concept is an important component of statistical inference. This question aims to give you the opportunity to revisit this concept. No calculation or computing are needed! Explain briefly in your own words what the following are. If you would like to include a diagram, please do, but it’s not necessary.

(a) The sampling distribution of the sample maximum.

(b) The mean of the sampling distribution of the sample maximum.

In your own words, describe why it wouldn’t be best to run multiple independent-sample t-tests when you have 3 or more groups. Come up with a sample experiment where you would use a between-subjects one-way ANOVA. Come up with a sample experiment where you would use a within-subjects one-way ANOVA. Why do we run post hoc tests? Under what conditions should you run a post hoc test?

I need this in R code please: Use the dataset ’juul’ in package ’ISwR’ to answer the question. (1) Conduct one-way ANOVA test to test if the mean of igf1 of each level of tanner are the same? (2) What is the mean of igf1 in each level of tanner? (3) If there is any difference, which ones appear to be different? (Use pairwise t test for each pair of level with bonferroni method)

What sample size would you need to make the 99% confidence interval have the same margin of error as the 90% confidence interval?

Describe how you would collect a sample that gave each person in the population an equal chance of being sampled.

Problem 1: Oil Production Data: The Data in the following are the annual world crude oil production in millions of barrels for the period 1880-1988. The data are taken from Moore and McCabe( 1993, p. 147).

Here is the code help you to paste the data into your R.

data5<-'year barrels
1880 30
1890 77
1900 149
1905 215
1910 328
1915 432
1920 689
1925 1069
1930 1412
1935 1655
1940 2150
1945 2595
1950 3803
1955 5626
1960 7674
1962 8882
1964 10310
1966 12016
1968 14104
1970 16690
1972 18584
1974 20389
1976 20188
1978 21922
1980 21722
1982 19411
1984 19837
1986 20246
1988 21388
'
data5n<-read.table(textConnection(object=data5),
header=TRUE,
sep="",
stringsAsFactors = FALSE)

1. Fit a linear regression line of log (OIL) on Year. Assess the goodness of fit of the model.
2. Construct the index plot of the standardized residuals. This graph shows clearly that one of the standard assumptions is violated. Which one?

1. Develop a revenue management (maximizing) model based on the information given in the scenario.
2. How many seats should be allocated to each of the 16 itineraries to maximize revenue?
3. What is the (maximum) expected revenue to be earned per day for all 16 flights?
4. Assume operating costs for each of the legs is as follows:
   1. Leg 1 = $20,250
   2. Leg 2 = $19,750
   3. Leg 3 = $20,500
   4. Leg 4 = $19,500

What is the expected operating income for each of the legs? And in total for Freedom Airlines, given these 16 itineraries?

How do I find the optimal seat allocation?

Question 1:

Dr. Snow replicated the previous study and obtained scores for the three samples listed in the table below:

In SPSS, analyze the data Dr. Snow collected using a one-way ANOVA.

Complete the table below using the results found in the output box labeled Descriptives, then use the response to complete the following 6 questions.

1. mean of the low HS group? (2 decimal places)
2. mean of the medium HS group? (2 decimal places)
3. mean of the high HS group? (2 decimal places)
4. SD of the low HS group? (2 decimal places)
5. SD of the medium HS group? (2 decimal places)
6. SD of the high HS group? (2 decimal places)
7. F-obtained values?
8. between-groups MS? (3 decimal places)
9. within-groups MS? (3 decimal places)
10. significance levels?
11. F ratio?(2 decimal places)
12. p value for Dr. Snow's study?(3 decimal places)
13. Write a complete APA-style conclusion for Question2.

Let X be the exam grade of a student taking Calculus 1 with Professor Smith. The professor believes that X has a mean of 81 and a standard deviation of 22. Suppose there are 100 students in Professor Smith's class.

Approximate the probability that X is higher than 83.6 OR smaller than 79.2?

Suppose there was no correlation between the Test Screen and the medical assessment of disease (i.e. the test was not able to differentiate between those with or without the disease). Based on the table given above, how many true positives among the sample of 100 do you expect the Test Screen to reveal? Based on this outcome and the observed values given in the initial table above, comment on the association between Test Screen and disease status.

                                   Medical Assessment

Test Screen              Disease          No Disease Total

Possible Disease   30                    20                    50

No Disease              10                    40                    50

Total                          40                    60                    100

Mrs. Warrack, a retired archeologist, enjoys hiking in Badger Creed every other day. Usually she travels 3 miles per hike. During the past year Mrs. Warrack has recorded the times of her hikes. For a sample of 90 times, the mean was x ̅=23.18 minutes and the standard deviation was s = 1.87 minutes. Let μ mean the mean hiking time for the entire distribution of Mrs. Warrack’s 3-mile hike times (taken over the past year )    

How many degrees of freedom are there?    

Find a 0.95 confidence interval μ. Use t*= 1.987 .

An engineer measured the Brinell hardness of 25 pieces of ductile iron from her company, that were subcritically annealed. She believes that the alloys her company uses in iron, will ultimately make the iron stronger, and thus will have a higher Brinell hardness score. She tests 25 pieces of ductile iron from her company with the resulting data of Brinell hardness scores:

170 167 174 179 179 187 179 183 179

156 163 156 187 156 167 156 174 170

183 179 174 179 170 159 187

The engineer hypothesizes that the mean Brinell hardness score of such ductile iron pieces from her company will greater than known average Brinell score for iron which is 170.

At the 5% level of significance, is there enough evidence to conclude this?

1) Step 1: State the Claims which means to State the null and alternative hypotheses. Use correct math type. You may want to consider looking back at the symbols assignment from the beginning of class.

2).

a) What is the sample mean? Use 4 decimal places.

b) What is the sample standard deviation? Use 4 decimal places.

c) Are the normality assumptions met?

3) Step 3: Assessment of Evidence. Find the pvalue and upload an image of the normal curve with the test statistic indicated and the correct area of the curve shaded. This shaded area is the pvalue.

a) What is the pvalue? Use 4 decimal places.

b) Upload an image of the normal curve with the test statistic indicated and the correct area of the curve shaded. This shaded area is the pvalue.

4) Step 4: Conclusion. State your conclusion. Either reject or fail to reject H0H0 , indicate why, then write the conclusion in terms of the problem.

Chemical signals of mice.Consider Refer to the Cell (May 14, 2010) study of the ability of a mouse to recognize the odor of a potential predator, Exercise 3.63 (p. 143). Recall that theThe sources of these odors are typically major urinary ­proteins (Mups). In an experiment, 40% of lab mice cells exposed to chemically produced cat Mups responded positively (i.e., recognized the danger of the lurking predator). Consider a sample of 100 lab mice cells, each exposed to chemically produced cat Mups. Let x represent the number of cells that respond positively. Explain why the probability distribution of x can be ­approximated by the binomial distribution. Find E(x) and interpret its value, practically. Find the variance of x. Give an interval that is likely to contain the value of x.