6. A random sample of 15 women’s resting pulse rates from the National Health and Nutrition

Examination Survey (NHANES) showed a mean of 73.5 beats per minute and standard deviation is 17.1

1. Assume that the pulse rates are Normally distributed.

1. (3 points) Find a 99% confidence interval for the population pulse rate of women. Write down what command you used and what numbers you entered.

(d) (2 points) Is it plausible that the population pulse rate for women is 80? Explain.

7. Pass rates for Intermediate Algebra at a community college are 52.6%. In an effort to improve pass rates in the course, faculty of the community college develop a mastery-based learning model where course content is delivered in a lab through a computer program. The instructor serves as a learning mentor for the students. Of the 480 students who enroll in the mastery-based course, 267 pass. Was the college’s effort to improve the pass rate successful? Use = 0.05.

1. (4 points) State the null and alternative hypotheses using both symbols and words (be sure to use the correct symbols).

2. (3 points) Show that the conditions for the CLT are satisfied.

3. (4 points) Perform the appropriate hypothesis test using technology. Write down what command you used and what numbers you entered. Report the values of the test statistic and p-value.

4. (1 point) Do you reject or fail to reject the null hypothesis?

(e) (2 points) State your conclusion in the context of this problem.

Calculate a 99% confidence interval for population proportion when the population proportion is 0.826 and n=92. Thank you!

Which of the following statements regarding t and z distributions is/are true? Correctany false statements to make them true.

A) The area under a t-distribution to the left of -1.97 is greater than the area to the right of 2.17 for a sample of any size.

B) The area under the curve (AUC) to the right of t=2.00 when n=15 is smaller than the AUC to the right of t=2.00 when n=50.

C) The t-curve has thinner tails and a smaller standard deviation than a normal distribution for small sample sizes.

D) When x and (n-x) are both ≥ 5, the sampling distribution of p̂ is approximately normally distributed and we use a t coefficient to calculate the margin of error for estimating a sample proportion.

E) When we standardized the sampling distribution of sample means using estimatedSEM = s/√n, the result is distributed as a standard normal distribution when n=35.

The Millennial generation (so called because they were born after 1980 and began to come of age around the year 2000) is less religiously active than older Americans. One of the questions in the General Social Survey in 2010 was "How often does the respondent pray?" Among the 419 respondents in the survey between 18 and 30 years of age, 277 prayed at least once a week. Assume that the sample is an SRS. Use the plus-four method to give a 99% confidence interval (±0.0001) for the proportion of all adults between 18 and 30 years of age who pray at least once a week. 99% confidence interval is from _ to _

Normal probability distribution

Is a continuous distribution

Review the in-class Excel worksheet and list criteria under which it is appropriate to use the normal distribution in the calculation of probabilities

Review the Excel Normal Distribution video clip in the In-class Excel folder. The feature needs the mean and the standard deviation of the distribution under study. Use Excel to calculate the following Normal distribution probabilities:

Mean = 5ft, standard deviation = .7ft. The probability that a woman’s height is over 5.7 ft

Mean = 126 1bs, standard deviation = 10 lbs. The probability that a woman’s weight is less than 110 lbs

Think about real life work or daily applications. Describe a situation that could possibly framed as a Normal distribution problem for which we can calculate probabilities. Please summaries your revision perspective here

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