a) What is the probability of rolling a 5 with a balanced die?

b) Find the number of ways in which a person can select 3 stocks from a list of 5 stocks?

c) What is probability of drawing a 5 from a well shuffled deck of 52 playing cards?

d) In how many ways can a principal choose 3 of 45 members to review a student grade appeal?

Below is the PSPP analysis for ages (in years) of all 50 heads of households in a small Nova Scotian fishing village. Refer to the PSPP outputs below and answer the related questions.

a) Interpret the standard deviation of age in the context of this study.

b) Suppose that we take a random sample of 36 heads of households. What would the sample data distribution tend to resemble more closely – the sampling distribution or the population distribution? Briefly Explain.

c) What do you expect for the mean of sample means in the long run of repeated samples of size 36?

d) What do you expect for the standard deviation of sample means in the long run of repeated samples of size 36? Show your work.

e) Explain the difference between a sample data distribution and the sampling distribution of sample mean.

f) Suppose that for a random sample of heads of households, we get a mean of 44.22, and standard deviation of 14.73. Before observing the sample, find the probability that our sample mean falls within 2.48 of the population mean. Interpret the result in the context of this problem.

Questions 8 and 9 are based on the following information:

A local retail business wishes to determine if there is a difference in the mean preferred indoor temperature between men and women. Assume that the population standard deviations of pre- ferred temperatures are equal between men and women. Two independent random samples are collected. Sample statistics of preferred temperatures are reported in the table below.

Standard deviation : Men: 1.2. Women : 1.4

In testing whether two population means are different, the value of test statistic is .

A. 1.255

B. 1.378

C. 1.405

D. 1.578

Suppose that we perform a two-tailed test of the difference of population means, which of the following is the correct conclusion?

A. At the 0.20 significance level, we reject the null hypothesis, there is a difference in the preferred indoor temperature between men and women.

B. At the 0.10 significance level, we reject the null hypothesis, there is a difference in the preferred indoor temperature between men and women.

C. At the 0.10 significance level, we fail to reject the null hypothesis, since the test statistic is smaller than the critical value 1.645.

D. There is in sufficient evidence to draw a conclusion on the test.

Think of (and describe) a problem in your work that can be addressed using a t test for two INDEPENDENT or two DEPENDENT/CORRELATED samples.

Clearly identify the independent and dependent variables. Note that the dependent variable must be continuous (interval or ratio). The independent variable must be dichotomous.

You observe the returns Rt (t = 1; 2; :::28) (in %) on your investment for the last 28 days (see the attached
Öle). Follow the steps explained in class to answer these questions:
What is the mean return (in %) on your investment, ? Explain.
Is lower than -1%? Explain.
Assume that = 0 and = 4. What is the probability that the next 30 days average return on your
investment will be greater than 1%? Explain. What is the probability that the next 15 days average return
on your investment will be greater than 1%? Explain.
Explain all the steps when answering the above questions.

Day Return % 1 0.17 2 0.64 3 -0.11 4 0.16 5 -0.26 6 0.48 7 -0.41 8 -1.03 9 -3.32 10 -3.03 11 -0.37 12 -4.49 13 -0.42 14 4.33 15 -2.86 16 4.2 17 -3.32 18 -1.65 19 -7.81 20 5.17 21 -4.87 22 -9.57 23 13.55 24 -17.94 25 5.4 26 -5.06 27 0.21 28 -4.31

Consider a possible linear relationship between two variables that you would like to explore.

1) Define the relationship of interest and a data collection technique.

2) Determine the appropriate sample size and collect the data.

3) Perform the appropriate analysis to determine if there is a statistically significant linear relationship between the two variables. Describe the relationship in terms of strength and direction.

4) Construct a model of the relationship and evaluate the validity of that model.

Provide complete sentence explanations for each of the above.

. Assume X ~ N (10, 4).

1. What is the (approximate) distribution of X if the sample size is 100? Briefly discuss the theorem underlying your answer.
2. What happens to the variance of as the sample size increases? Draw a diagram and explain.
3. What two values of (symmetric around the population mean) contain a) 75% and b) 95% of the distribution? Draw a diagram. Relate your answer to b) to the empirical rule.

5, Determine the area under the standard normal curve that lies to the right of ​(a) Z = -0.95 , ​(b) Z=0.53, ​(c)  Z =−0.05, and ​(d) Z =−0.89.

​(a) The area to the right of Z=−0.95 is ____.

​(Round to four decimal places as​ needed.)

​(b) The area to the right of Z=0.53 is _____.

​(Round to four decimal places as​ needed.)

​(c) The area to the right of Z=−0.05 is _____.

​(Round to four decimal places as​ needed.)

​(d) The area to the right of Z=−0.89 is _____..

​(Round to four decimal places as​ needed.)

6,  Determine the area under the standard normal curve that lies between ​(a)  Z =−0.53 and Z=0.53 ​, ​(b)  Z=−2.67 and Z=0​, ​(c)  Z =−0.87 and Z =0.93.

​(a) The area that lies between Z =−0.53 and  Z  =0.53 is ____.

​(Round to four decimal places as​ needed.)

​(b) The area that lies between  Z =−2.67 and  Z =0 is ___.

​(Round to four decimal places as​ needed.)

​(c) The area that lies between  Z =−0.87 and Z =0.93 is _____.

​(Round to four decimal places as​ needed.)

13, A survey was conducted that asked 998 people how many books they had read in the past year. Results indicated that x overbar =13.513.5 books and s =16.1 books. Construct a 95​% confidence interval for the mean number of books people read. Interpret the interval.

(Use ascending order. Round to two decimal places as​ needed.)

A.

If repeated samples are​ taken, 95​% of them will have a sample mean between ___ and ____.

B.

There is 95​% confidence that the population mean number of books read is between ___ and ____.

C.

There is a 95​% probability that the true mean number of books read is between ___ and ___.

18, Steel rods are manufactured with a mean length of 26 centimeter​ (cm). Because of variability in the manufacturing​ process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Complete parts ​(a) to ​(d).

​(a) What proportion of rods has a length less than 25..9 ​cm?

nothing ​(Round to four decimal places as​ needed.)

​(b) Any rods that are shorter than 25.87 cm or longer than 26.13 cm are discarded. What proportion of rods will be​ discarded?

nothing ​(Round to four decimal places as​ needed.)____​(Round to four decimal places as​ needed.)

​(c) Using the results of part ​(b)​, if 5000 rods are manufactured in a​ day, how many should the plant manager expect to​ discard?

____​(Use the answer from part b to find this answer. Round to the nearest integer as​ needed.)

​(d) If an order comes in for 10,000 steel​ rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 25.9 cm and 26.1 cm?

___ ​(Round up to the nearest​ integer.)

19, According to a​ study, 59​% of all males between the ages of 18 and 24 live at home. ​ (Unmarried college students living in a dorm are counted as living at​ home.) Suppose that a survey is administered and 163 of 248 respondents indicated that they live at home.​ (a) Use the normal approximation to the binomial to approximate the probability that at least 163 respondents live at home.​ (b) Do the results from part​ (a) contradict the​ study?

​(a) ​P(X≥163​)=___​(Round to four decimal places as​ needed.)

​(b) Does the result from part​ (a) contradict the results of the​ study?

A.

Yes​, because the probability of ​P(X≥163163​) is greater than 0.05 .

B.

Yes​, because the probability of ​P(X≥163​) is less than 0.05

C.

No, because the probability of ​P(X≥163​) is less than 0.05 .

D.

No​, because the probability of ​P(X≥163​) is greater than 0.05.

The length of time it takes a baseball player to swing a bat (in seconds) is a continuous random variable X with probability density function (p.d.f.) f(x) = ( ax + 8/9 for 0 ≤ x ≤ b

(c) Calculate (to 3 decimal places of accuracy) the median of X.

(d) What is the probability that the baseball player takes between 5 and 10 swings (inclusive) before a swing whose length is greater than the median in part (c) occurs for the first time?

(e) Over the next 36 (independent) swings that the baseball player takes, what is the approximate probability that the average swing length is between 3/5 and 4/5 of a second?

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The problem and questio

Analysis of Variance by hand. The average number of purchases in three different stores are compared to determine if they are significantly different. The following summary statistics is given for each store. State the null and alternative hypothesis, calculate the F-statistics, p-value, and give a concluding statement.

Table of values: Three different stores

Summarize your calculations in an ANOVA table below, and SHOW YOUR WORK COMPLETELY.

The subject is statistics

Chapter 6 Homework

Required information

Exercise 6A-2 Least-Squares Regression [LO6-11]

[The following information applies to the questions displayed below.]

Bargain Rental Car offers rental cars in an off-airport location near a major tourist destination in California. Management would like to better understand the variable and fixed portions of its car washing costs. The company operates its own car wash facility in which each rental car that is returned is thoroughly cleaned before being released for rental to another customer. Management believes that the variable portion of its car washing costs relates to the number of rental returns. Accordingly, the following data have been compiled:

Exercise 6A-2 Part 2

2. Using least-squares regression, estimate the variable cost per rental return and the monthly fixed cost incurred to wash cars. (Round your Fixed cost to the nearest whole dollar amount and the Variable cost per unit to 2 decimal places.)

Describe when you believe it is appropriate to use the following terms in developing data reports for a healthcare organization: mean, median and mode. Why?

The world's smallest mammal is the bumblebee bat. The mean weight of 40 randomly selected bumblebee bats is 1.659 grams, with a standard deviation of 0.264 grams.
Find a 99.9% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):

Find a 99% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):

Find a 95% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):

Find an 80% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):

Describe an application of multiple discriminant analysis that is specific to scientific research or to your academic interests. Explain why this technique is suitable in terms of measurement scale of variables and their roles.

We know that based on the Binomial distribution, probability of x successes in n trials when the probability of success is (p) can be calculated by multiplying Combinations of n items x by x, multiplied by the probability of success (p) raised to (x) and multiplied by (1-p) raised to (n-x).

1. If probability of having a child who will study business in college (probability of success) is 0.25, what is the probability of a family with 6 children will have 3 of them study business in college

2. If probability of catching a cold is 0.03, what is the probability of 3 people out of six catching a cold?

3. If probability of catching a cold is 0.97, what is the probability of 3 people out of six catching a cold?