1. The distribution of diastolic blood pressures for the population of female diabetics between the ages of 30 and 34 has an unknown mean and standard deviation.  A sample of 10 diabetic women is selected; their mean diastolic blood pressure is 84 mm Hg. We want to determine whether the diastolic blood pressure of female diabetics are different from the general population of females in this age group, where the mean μ = 74.4 mmHg and standard deviation σ = 9.1 mm Hg.  Diastolic blood pressure is normally distributed.    
a) Create a two-sided 95% confidence interval to determine whether diabetic women have a different mean diastolic blood pressure compared to the general population.   
b) Now, conduct a two-sided hypothesis test at the α = 0.05 level of significance to determine whether diabetic women have a different mean diastolic blood pressure compared to the general population.  Use both critical value and p-value methods.
For either method, would your conclusion have been different if you had chosen α = 0.01 instead of α = 0.05?

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 9 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:

a. What is a point estimate for the population mean length of time. (Round answer to 4 decimal places)

b. Which distribution should you use for this problem?

• normal distribution
• t-distribution

c. Why?


d. What must be true in order to construct a confidence interval in this situation?

• The population must be approximately normal
• The sample size must be greater than 30
• The population mean must be known
• The population standard deviation must be known

e. Construct a 98% confidence interval for the population mean length of time. Enter your answer as an open-interval (i.e., parentheses) Round upper and lower bounds to two decimal places

f. Interpret the confidence interval in a complete sentence. Make sure you include units

g. What does it mean to be "98% confident" in this problem? Use the definition of confidence level.

• There is a 98% chance that the confidence interval contains the population mean
• 98% of all simple random samples of size 9 from this population will result in confidence intervals that contain the population mean
• The confidence interval contains 98% of all samples

h. Suppose that the company releases a statement that the mean time for all patients is 2 hours.

Is this possible?

• Yes
• No

Is it likely?

• No
• Yes

i. Use the results above and make an argument in favor or against the company's statement. Structure your essay as follows:

1. Describe the population and parameter for this situation.
2. Describe the sample and statistic for this situation.
3. Give a brief explanation of what a confidence interval is.
4. Explain what type of confidence interval you can make in this situation and why.
5. Interpret the confidence interval for this situation.
6. Restate the company's claim and whether you agree with it or not.
7. Use the confidence interval to estimate the likelihood of the company's claim being true.
8. Suggest what the company should do.

The pth percentile (0 < p < 100) of a random variable X is a number m that satisfies FX(m) = p/100. Find the 25th , 50th (median), and 75th percentiles of the exponential random variable with parameter λ. Find the same for a normal random variable with mean µ and standard deviation σ.

1. In a study of police gunfire reports during a recent year, it was found that among 540 shots fired by New York City police, 182 hit their targets; and among 283 shots fired by Los Angeles police, 77 hit their targets.

a. Use a 0.05 significance level to tes t the claim that New York City police and Los Angeles

police have different proportion of hits.

b. Construct a 90 % confidence interval to estimate the difference between the two

proportions of hits.

Corporate triple A bond interest rates for 12 consecutive months are as follows: 9.7 9.4 9.6 9.8 9.6 9.9 9.9 10.5 9.8 9.5 9.4 9.4 If required, round your answer to two decimal places. (a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data? (b) Develop three-month and four-month moving averages for this time series. If required, round your answers to two decimal places. Week Sales 3 Month Moving Average 4 Month Moving Average 1 9.7 2 9.4 3 9.6 4 9.8 5 9.6 6 9.9 7 9.9 8 10.5 9 9.8 10 9.5 11 9.4 12 9.4 3-month moving average 4-month moving average MSE Does the three-month or the four-month moving average provide the better forecasts based on MSE? Explain. (c) What is the moving average forecast for the next month?

(Round all intermediate calculations to at least 4 decimal places.)

Consider the following hypotheses: H0: μ = 40 HA: μ ≠ 40

Approximate the p-value for this test based on the following sample information. Use Table 2.

a. x⎯⎯ = 37; s = 9.1; n = 16

0.20 < p-value < 0.40

0.10 < p-value < 0.20

0.05 < p-value < 0.10

p-value < 0.05

p-value > 0.4

b. x⎯⎯ = 43; s = 9.1; n = 16

0.20 < p-value < 0.40

0.10< p-value < 0.20

0.05 < p-value < 0.10

p-value < 0.05

p-value Picture 0.4

c. x⎯⎯ = 37; s = 8.9; n = 15

0.20 < p-value < 0.40

0.01 < p-value < 0.03

0.05 < p-value < 0.10

p-value < 0.01

p-value Picture 0.4

d. x⎯⎯ = 37; s = 8.9; n = 29

0.05 < p-value < 0.10

0.10 < p-value < 0.20

0.03 < p-value < 0.05

p-value < 0.025

p-value Picture 0.2

2. Suppose body mass index (BMI) varies approximately to the normal distribution in a population of boys aged 2-20 years. A national survey analyzed the BMI for American adolescents in this age range and found the µ=17.8 and the σ=1.9. a) What is the 25th percentile of this distribution? (1 point) b) What is the z-score corresponding to finding a boy with at least a BMI of 19.27? (2 points) c) What is the probability of finding a boy with at least this BMI? (2 points)

2.) Find the 90% confidence intervals for population mean for the following a.) sample mean is 53 and  = 7.1 for n = 90 b.) sample mean is 285 and  = 7.1 for n = 28 c.) sample mean is 149.7 and s = 23.8 for n = 20

A poll is taken in which 349 out of 500 randomly selected voters indicated their preference for a certain candidate. (a) Find a 99% confidence interval for p. ≤p≤ (b) Find the margin of error for this 99% confidence interval for p.

A normal distribution has a mean of µ = 28 with σ = 5. Find the scores associated with the following regions:

a. the score needed to be in the top 41% of the distribution b. the score needed to be in the top 72% of the distribution c. the scores that mark off the middle 60% of the distribution

A teacher is explaining to her class the concepts of genetics regarding eye color.

She assumes that categories will have the following proportions: Blue = 20%, Green = 10%, Brown = 50%, Hazel = 20%

Use a 0.05 level of significance.

Here are the results for the class.

Observed Eye Colors: Blue=4; Green=3; Brown= 9, Hazel= 4,

What test are you running?

What are the observed values for the blue eye, brown eye, hazel eye color?

What are the expected values for the blue eye color, green eye color, brown eye color, and hazel eye color?

What are the degrees of freedom?

What is the null hypothesis?
What is the alternative hypothesis?

What is the test statistic? Use one decimal place.

What is the p-value? Use three decimal places.

What is your conclusion based on the p-value and the level of significance?

At the 5% significance level, what can you conclude?

According to a poll of Canadian adults, about 55% work during their summer vacation. Consider a sample of 150 adults,

a. What is the probability that between 49 and 60% of the sampled adults work during the summer vacation?

b. What is the probability that over 62% of the sampled adults work during summer vacation?

c. Calculate a 95% CI for the population proportion p.

d. We would need to calculate a [X]% CI to modify the margin of error to 0.1418.

e. In order to maintain the 95% CI while having a margin of error equal 0.1418, we need to change our sample size from 150 to [X].

An underprepared student takes a 8 question multiple choice quiz by guessing every answer. There are 5 choices (a,b,c,d,e). answer the following... what is p1, p2 and n (a). the average number of correct questions. (b). the standard deviation in correct question. (c) the probability of no questions correct. (e) the probability of getting at least 1 correct. (f) the probability of getting fewer than 3 questions correct. (g) the probability of getting exactly half correct.

A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task is faster if they are wearing ear buds.   A random sample of 20 workers' times were collected before and after wearing ear buds. Test the claim that the time to complete the task will be faster, i.e. meaning has production increased, at a significance level of α = 0.01

For the context of this problem, μ_D = μ_before−μ_after where the first data set represents before ear buds and the second data set represents the after ear buds. Assume the population is normally distributed. The hypotheses are:

H₀: μ_D = 0
H₁: μ_D > 0

You obtain the following sample data:

a) Find the p-value. Round answer to 4 decimal places.

Answer:

b) Choose the correct decision and summary.

A trucking company determined that the distance traveled per truck per year is normally​ distributed, with a mean of 80 thousand miles and a standard deviation of 10 thousand miles. Complete parts​ (a) through​ (c) below. a. nbsp What proportion of trucks can be expected to travel between 66 and 80 thousand miles in a​ year? The proportion of trucks that can be expected to travel between 66 and 80 thousand miles in a year is . 4192. ​(Round to four decimal places as​ needed.) b. nbsp What percentage of trucks can be expected to travel either less than 55 or more than 95 thousand miles in a​ year? The percentage of trucks that can be expected to travel either less than 55 or more than 95 thousand miles in a year is 7.30​%. ​(Round to two decimal places as​ needed.) c. nbsp How many miles will be traveled by at least 85​% of the​ trucks? The amount of miles that will be traveled by at least 85​% of the trucks is nothing miles. ​(Round to the nearest mile as​ needed.)