Determine the area under the standard normal curve that lies between:

a. z= -.31 and z=1.61

b. z=-2.01 and z=.26

c. z=-1.20 and z=2.11

d. z=1.92 and z=2.43

Find the value of z_a

a. z_.56=

b. Z_.23=

c. Z_.81=

d. Z_.06=

5.) For the data set

(a) Find the 80th percentile.

(a) Find the 42nd percentile.

(a) Find the 17th percentile.

(a) Find the 65th percentile.

6.) Internet providers: In a survey of 672 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $52.8 with standard deviation $12.42 Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $40.38 and $65.22

The table below lists a random sample of 50 speeding tickets on I-25 in Colorado.

Round to the fourth.
a) If a random ticket was selected, what would be the probability that the driver was female?
b) Given that a particular ticket had a male offender, what is the probability that they were more than 20 mph over the limit?
c) Given that a particular ticket was 10-20 mph over the limit, what is the probability that the driver was female?
d) If a random ticket was selected, what would be the probability that the driver was a male?
e) If a random ticket was selected, what would be the probability that the driver is a female and driving 10-20 mph over the limit?
f) If a random ticket was selected, what would be the probability that the driver is a female or driving 0-10 mph over the limit?

Chapter 3 – Numerically Summarizing Data

1. Section 3.1 Measures of Central Tendency

pH in Water:

The acidity of alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water.

1. Determine the mean, median and mode pH for each type of water.
2. Comment on the differences between the two water types.
3. Suppose the pH of 7.10 in tap water was incorrectly recorded as 1.70. How does this affect the mean? The median?
4. What property of the median does this illustrate?

2. Section 3.2 Measures of Dispersion

pH in Water:

Use the same pH data table in the above question to answer the following.

1. Which type of water has more dispersion in pH using the range as the measure of dispersion?
2. Which type of water has more dispersion in pH using the standard deviation as the measure of dispersion?

3. Section 3.2 Measures of Dispersion

The Empirical Rule:

SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114.

1. What percentage of SAT scores is between 401 and 629?
2. What percentage of SAT scores is less than 401 or greater than 629?

4. Section 3.4 Measures of Position and Outliers

You Explain it – Percentiles & Quartiles:

1. The 5^thpercentile of the weight of males 36 months of age is 12.0 kg.
2. The 95^thpercentile of the length of newborn females is 53.8 cm.

One variable that is measured by online homework systems is the amount of time a student spends on homework for each section of the text. The following is a summary of the number of minutes a student spends for each section of the text for the fall 2014 semester in a college statistics class at UHWO.

Q1 = 42         Q2 = 51.5         Q3 = 72.5

3. Provide an interpretation of these results.
4. Determine and interpret the interquartile range.
5. Suppose a student spends 2 hours doing homework for a section. Is this an outlier?
6. Do you believe that the distribution of time spend doing homework is skewed or symmetric? Explain your answer.

5. Section 3.5 The Five Number Summary & Boxplots

Got a Headache?

The following data represent the weight in grams of a random sample of 25 Tylenol tablets.

1. Construct a boxplot.
2. Use the boxplot and quartiles to describe the shape of the distribution.

(A review on SAS data management) The following is a data set of 12 individuals. And we want to relate the heart rate at rest (Y) to kilograms body weight (X). X Y 90 62 87 41 87 63 73 46 73 53 86 55 100 70 75 47 76 49 87 69 79 41 78 48 Write a program in SAS which read the given data set into SAS library. In your program, create a new data set which is a copy of the first, with the addition of a new variable which represents the weight in pounds (1 kilogram≈2.2 pounds). Use “proc print” to view the data for all three variables. (c) Create a new variable called weight_group which divides the data set into four groups based on the estimated quartiles for the variable weight. The estimated quartiles may be requested using the keywords q1, median, and q3, in the “proc means” statement. (d) Use “proc freq” to summarize the frequency of subjects in each of the four groups. (e) Obtain the mean and standard deviation for the heart rate at rest for each of the four groups. Comment on the results. (f) Produce a scatterplot of the heart rate at rest versus body weight in kilograms. Describe what you see. (g)Fit a straight line model for heart rate at rest versus body weight in kilograms. Comment on the fit of the line.

What does the sigma level capability mean for a process? Explain at least two reasons for the importance of achieving six-sigma capability. explain in detail

From your analysis of Desertia, you conclude that citizens there average $1,000 per month in household disposable income. The Minister of Development for Mountania says that disposable income is the same in his country. To see if the data supports this, your company has sampled 100 households from Mountania and obtained data on household disposable income. Use the Data provided to:

a. ​Derive a frequency distribution of income. Divide by 8
b.​Create a histogram of income
c.​Obtain and fully interpret/explain the sample mean and standard deviation
d.​Test the hypothesis, at the 5% significance level, that Mountania also has a mean of $1,000

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

Test the following hypotheses by using the

χ²

goodness of fit test.

A sample of size 200 yielded 80 in category A, 20 in category B, and 100 in category C. Use α = 0.01 and test to see whether the proportions are as stated in

H₀.

(a)

Use the p-value approach.

Find the value of the test statistic.

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.     Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.

(b)

Repeat the test using the critical value approach.

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.)

test statistic ≤test statistic ≥

State your conclusion.

Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.     Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.

The college bookstore tells prospective students that the average cost of its textbooks is $108 with a standard deviation of $4.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students will select a random sample of size 100. Assume that the mean from their random sample is $112.80.

1. Perform a hypothesis test (using R) at the 5% level of significance and state your decision. Also construct a 90% confidence interval (using R) for the average cost of textbook.
2. Perform the above task under the assumption that the students selected a random sample of size 10.
3. Write the difference between your findings of (1) and (2).

1. A clinician claims that, on average, the blood pressure of hypertensive patients is 150. A particular doctor believes the amount is more than 150. Then he selected a random sample of 100 patients and found that the sample have average of 155 with standard deviation of 10. Conduct the test at the 0.05 of significance. a) Hypotheses HO: vs. HA a) Test statistic b) P-value c) Conclusion d) What is the power of the test conditions to identify a significant difference if the population mean was actually 152 at α=0.05 (two sided)? e) How large a sample is needed for a one-sample z test with 80% power and α = 0.05 (two-tailed) when σ = 10?

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

A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: the company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows.

(a)

Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company.

State the null and alternative hypotheses.

H₀: Employment plan is mutually exclusive from the type of company.
H_a: Employment plan is not mutually exclusive from the type of company.H₀: Employment plan is not independent of the type of company.
H_a: Employment plan is independent of the type of company.     H₀: Employment plan is not mutually exclusive from the type of company.
H_a: Employment plan is mutually exclusive from the type of company.H₀: Employment plan is independent of the type of company.
H_a: Employment plan is not independent of the type of company.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

At a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We cannot conclude that the employment plan and the type of company are not independent.Reject H₀. We conclude that the employment plan is not independent of the type of company.     Reject H₀. We conclude that the employment plan is independent of the type of company.Do not reject H₀. We cannot conclude that the employment plan and the type of company are independent.

(b)

Discuss any differences in the employment plans for private and public companies over the next 12 months. (Round your numeric answers to two decimal places.)

Employment opportunities look to be much better for public companies, while private companies have the greater proportions of "no change" and "lay off employees" planned.Employment opportunities look to be much better for private companies, while public companies have the greater proportions of "no change" and "lay off employees" planned.     Employment opportunities look to be about the same for both public and private companies, with high proportions of "no change" and "lay off employees" planned for both.Employment opportunities look to be about the same for both public and private companies, with high proportions of "add employees" planned for both.

Assume that 15% of circuit boards used in manufacturing compact displayers are defective. Off a batch of 200 randomly selected such circuit boards, use the normal approximation with the continuity correction to find the probability that at most 30 of these boards are defective. Is your answer approximate or exact.

b. find exact probability using R code to compare answer on the previous question?

Please do in Excel

A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 p.m. lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected and the waiting times are collected and stored in Bank1 . These data are:

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20

4.50 6.10 0.38 5.12 6.46 6.19 3.79

Suppose that another branch, located in a residential area, is also concerned with the noon-to-1 p.m. lunch period. A random sample of 15 customers is selected and the waiting times are collected and stored in Bank2 . These data are:

9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35

10.49 6.68 5.64 4.08 6.17 9.91 5.47

a. Is there evidence of a difference in the variability of the waiting time between the two branches? (Use a = 0.05.)

b. Determine the p-value in (a) and interpret its meaning.

c. What assumption about the population distribution of each bank is necessary in (a)? Is the assumption valid for these data?

d. Based on the results of (a), is it appropriate to use the pooled-variance t test to compare the means of the two branches?

The Reviews editor for a certain scientific journal decides whether the review for any particular book should be short (1–2 pages), medium (3–4 pages), or long (5–6 pages). Data on recent reviews indicates that 60% of them are short, 30% are medium, and the other 10% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 80% are in Word, whereas 40% of medium reviews are in Word and 30% of long reviews are in Word. Suppose a recent review is randomly selected.

a)What is the probability that the selected review was submitted in Word format?

b)If the selected review was submitted in Word format, what are the posterior probabilities of it being short, medium, or long? (Round your answers to three decimal places.)