Consider the experiment of rolling two dice and the following events:

    A: 'The sum of the dice is 8' and  B: 'The first die is an odd number' and C:  "The difference (absolute value) of the dice is 2"

Find  (a)  p(A and B) (HINT: You cannot assume these are independent events.)

       (b)  p(A or B)

        (c)  Are A and B mutually exclusive events? Explain.

(d)   Are A and B independent events? Explain.

(e)   Are B and C independent events? Explain.

M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows.

Color: Purple 23%, Yellow 19%, Red 22%, Orange 9%, Green 6%, Blue 6%, Brown 15%

Suppose you have a large bag of plain M&M candies and you choose one candy at random.

(a) Find P(green candy or blue candy).

Are these outcomes mutually exclusive? Why?

A. Yes. Choosing a green and blue M&M is not possible.

B. No. Choosing a green and blue M&M is not possible.    

C. Yes. Choosing a green and blue M&M is possible.

D. No. Choosing a green and blue M&M is possible.

(b) Find P(yellow candy or red candy).

Are these outcomes mutually exclusive? Why?

A. Yes. Choosing a yellow and red M&M is possible.

B. Yes. Choosing a yellow and red M&M is not possible.   

C. No. Choosing a yellow and red M&M is not possible.

D. No. Choosing a yellow and red M&M is possible.

(c) Find P(not purple candy).

1. An SRS of 16 households is selected in Houston and the number of remote controls is counted. We are interested in a hypothesis test that tests if population mean number of remote controls is greater than 5. In the sample, the mean number of remote controls is 7. The degrees of freedom associated with the test is: [2]
   1. 16
   2. 15
   3. 7
   4. 5
   5. Not enough information

2. Question 1 above yields a test statistic of 2. Circle all levels of significance that would result in a conclusion that rejects the null hypothesis. [2]
   1. 10%
   2. 5%
   3. 1%
   4. 0.5%
   5. Not enough information

3. Based on the information provided in question 1, if we reject the null hypothesis then 7 will be in corresponding confidence interval. [2]
   1. True
   2. False
4. Assume that we rejected the null hypothesis in the test referenced in questions 1-3. If we find out that the null hypothesis was actually true, what error did we make? [2]

Almost all employees working for financial companies in New York City receive large bonuses at the end of the year. A sample of 63 employees selected from financial companies in New York City showed that they received an average bonus of $56,000 last year with a standard deviation of $16,000. Construct a 98% confidence interval for the average bonus that all employees working for financial companies in New York City received last year.

Round your answers to cents.

$_____ to $_____

A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 114 homeowners selected from this area showed that they pay an average of $1579 per month for their mortgages. The population standard deviation of such mortgages is $213.

Find a 95% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area.

Round your answers to two decimal places.

____to____  dollars

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

A simple random sample of 50 items from a population with

σ = 8

resulted in a sample mean of 38. (Round your answers to two decimal places.)

(a)

Provide a 90% confidence interval for the population mean.

to

(b)

Provide a 95% confidence interval for the population mean.

to

(c)

Provide a 99% confidence interval for the population mean.

to

Assume a normal distribution and find the following probabilities. (Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x < 18 | μ = 22 and σ = 3)

(b) P(x ≥ 69 | μ = 50 and σ = 7)

(c) P(x > 43 | μ = 50 and σ = 5)

(d) P(18 < x < 22 | μ = 20 and σ = 3)

(e) P(x ≥ 96 | μ = 80 and σ = 1.77)

A manufacturer claims that the average tar content of a certain kind of cigarette is μ = 14.0. In an attempt to show that it differs from this value, five measurements are made of the tar content (mg per cigarette):

Construct a 99% confidence interval for the variance of the population sampled.

A market research firm conducts telephone surveys with a 47% historical response rate. If 75 individuals are contacted, find the probability that 36 or less of them will cooperate and respond to the survey questions.

When do I use:

Geometric cdf

Geometric pdf

binomial cdf

Binomial pdf

Thank you

In each of the following areas, what're two examples of how data accuracy can be compromised by inappropriate choices of the researcher;

a. Survey questionnaire design

b. Sampling plan for a survey

c. Data collection and recording

A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 40 households from the city, which gave the mean water usage to be 3411.10 gallons over a one-month period. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is 387.70 gallons. Make a 95% confidence interval for the average monthly residential water usage for all households in this city.

Round your answers to two decimal places.

_____ to_____  gallons

A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 205 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let XiXi , i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.

1-Find P( X1X1  > 100).

2-Find P( X1X1 > 100 and   X2X2 > 100 and • • • and   X5X5 > 100).

Easy Talk phones have an electronic component that is produced by WiredUp Inc. Under normal operations 8% of these components are defective. Every week, the production process is tested by inspecting 10 of the new components produced. If 2 (or 20%) or more are defective they shut down the production process for further inspection. The null and alternative hypotheses of the test are:

(null) H0 : π = 0.08

(alternative) Ha : π > 0.08

Where π is the proportion of components being produced that are defective at the time of the test.

(a) What is the test statistic that is being used in the test?

(b) What is the rejection region?

(c) Use an appropriate applet to determine the probability they make a Type I Error and shut down the production process unnecessarily.

(d) Suppose the machines producing the electronic component get out of adjustment and 15% of the components being produced are defective. Use an appropriate applet to find the probability the test will reveal that the machine is out of adjustment.

(e) Now use a theory-based method (and not an applet) to calculate the probability in (d) again.

(f) Both the calculations in (d) and (e) are approximate. Which do you expect to be more accurate? Explain.

(g) Suppose the change from an 8% to 15% defective rate is important for the company to detect. Briefly describe how the company might modify the test, without increasing the probability of a Type I Error, to increase the probability of detecting that the alternative hypothesis is true when the defective rate is 15%.