The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.29, 0.17, 0.25, 0.07, and 0.22.

1. Show the probability distribution for the expense forecast.
   

   x	f(x)
   9
   10
   11
   12
   13

   
   
2. What is the expected value of the expense forecast for the coming year (to 2 decimals)?
   
   
3. What is the variance of the expense forecast for the coming year (to 2 decimals)?
   
   
4. If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)?

Use the sample information x⎯⎯x = 36, σ = 7, n = 16 to calculate the following confidence intervals for μ assuming the sample is from a normal population.

(a) 90 percent confidence. (Round your answers to 4 decimal places.)

The 90% confidence interval is from  to

(b) 95 percent confidence. (Round your answers to 4 decimal places.)

The 95% confidence interval is from  to

(c) 99 percent confidence. (Round your answers to 4 decimal places.)

The 99% confidence interval is from  to

(d) Describe how the intervals change as you increase the confidence level.

Consider two independent random samples with the following results:

n1=532x1=390   

n2=730x2=139

Use this data to find the 90% confidence interval for the true difference between the population proportions.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3: Find the margin of error. Round your answer to six decimal places.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to three decimal places.

Using chi-square, test the null hypothesis that the prevalence of serious mental illness does not differ by type of substance abuse.

A sample of 118 college students is asked whether they are involved in campus activities. Using the following cross tabulation depicting student responses by the region in which their colleges are located, conduct a chi-square test of significance for regional differences.

Campus Activity Participation

Region     Involved      Uninvolved

East            19                     10

South         25                      6

Midwest        15                   15

West              8                       20

An internet search engine looks for a certain keyword in a sequence of independent websites. It is believed that 35% of the sites contain this keyword.

(a) Let X be the number of websites visited until the first keyword is found. Compute the probability that the search engine had to visit at least 10 sites in order to find the first occurrence of the keyword.

(b) Out of the first 25 websites, let Y be the number of sites that contain the keyword. Compute the probability that at least 10 of the first 25 websites contain the keyword.

A used car dealer says that the mean price of a three-year-old sport utility vehicle in good condition is $18,000. A random sample of 20 such vehicles has a mean price of $18,450 and a standard deviation of $1930. At α=0.08, can the dealer’s claim be supported? No, since the test statistic of 1.04 is close to the critical value of 1.24, the null is not rejected. The claim is the null, so is supported Yes, since the test statistic of 1.04 is not in the rejection region defined by the critical value of 1.85, the null is not rejected. The claim is the null, so is supported Yes, since the test statistic of 1.04 is in the rejection region defined by the critical value of 1.46, the null is rejected. The claim is the null, so is supported No, since the test statistic of 1.04 is in the rejection region defined by the critical value of 1.85, the null is rejected. The claim is the null, so is not supported

Assuming, I'm correct that sex and yes/no questions are nominal data, then the best source of testing from my reading and research is mode. However in my question/answers, the only options are mean, SD, range, or median. My reading and research says you can't use median, SD, or median. But range wouldn't really be relavent data either? The question does say "relative data". So my best guess is range; but I'm a bit confused by this? Can you shed any light into this question?  

Given are five observations for two variables, and . xi1 2 3 4 5 yi4 7 6 12 14 The estimated regression equation for these data is . a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSE SST SSR b. Compute the coefficient of determination (to 3 decimals). Does this least squares line provide a good fit? c. Compute the sample correlation coefficient (to 4 decimals).

Dihybrid crosses involving plants with either white or yellow flower and either tall or short morphs were done. The yellow allele is dominant over the while allele, and the tall allele is dominant over the short allele. The following are the observed numbers of each combination. Do these data fit the expected distribution? (3 points) Туре Yellow, Tall Yellow, Short Obs Exp 84 0.5625 54 0.1875 0.1875 White, Tall 40 White, Short 0.0625 22 a) What statistical test will you use? b) If needed, does your data have equal variance? Put "N/A" if not needed. Do you need to transform your data? If yes, does transformed data have equal variance? c) H: statistical and explanatory HA: statistical and explanatory d) p-value? Accept or reject null hypothesis? Discuss results of your data (patterns, post-hoc test, etc):

The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year. But let’s assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100. An educational researcher wants to estimate the mean SAT math score (μ) for his state this year.

The researcher chooses a random sample of 698 exams in his state. The sample mean for the test is 489. Find the 99% confidence interval to estimate the mean SAT math score in this state for this year. (Note: The critical z -value to use is: 2.576.) Your answer should be rounded to 3 decimal places.

DATAfile: CorporateBonds

You may need to use the appropriate appendix table or technology to answer this question.

A sample containing years to maturity and yield for 40 corporate bonds are contained in the data file named CorporateBonds.† (Round your answers to four decimal places.)

(a)

What is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?

x=  yrs=  yr

(b)

Develop a 95% confidence interval for the population mean years to maturity.

yr to  yr

(c)

What is the sample mean yield on corporate bonds and what is the sample standard deviation?

x=  % s=  %

(d)

Develop a 95% confidence interval for the population mean yield on corporate bonds.

__________ % to  % _____________

The following data represent the asking price of a simple random sample of homes for sale. Construct a 99​% confidence interval with and without the outlier included. Comment on the effect the outlier has on the confidence interval.

$270,500 , $143,000 , $459,900 , $208,500 , $279,900 , $205,800 , $283,900 , $147,800 , $219,900 , $248,900 , $187,500 , $264,900

Use the weights of cans of generic soda as sample​ one, and use the weights of cans of the diet version of that soda as sample two. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Construct a 99​% confidence interval estimate of the difference between the mean weight of the cans of generic soda and the mean weight of cans of the diet version of that soda. Does there appear to be a difference between the mean​ weights?

Assume that population 1 is the generic soda and population 2 is the diet soda.

The 99​% confidence interval is ____  ounces < μ1- μ2 < _____ ounces.
​(Round to four decimal places as​ needed.)