Lying to a teacher. One of the questions in a survey of high school students asked about lying to teachers. The following table gives the number of students who said that they lied to a teacher as least once during the past year, classified by sex:

A. Add the marginal totals to the table

B. Calculate appropriate percents to describe the results of this question

C. Summarize your findings in a short paragraph.

D. Test the null hypothesis that there is no association between sex and lying to teachers. Give the test statistics and the p-value with a sketch similar to the one on page 535 and summarize your conclusion. Be sure to include numerical and graphical summaries.

E. The survey asked student if they lied, but we do not know if they answered the question truthfully. How does this fact affect the conclusions that you can draw from this data?

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those​ tests, with the measurements given in hic​ (standard head injury condition​ units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified​ requirement?

724    660     1157     575     552     442

Identify test statistic

identify P value

State conclusion

coffee tea juice

Do a One-way ANOVA by hand (at least once in your life!) …Is there a difference in attention for those who drink coffee, tea, or juice during an 8 a.m. class? Utilize the five steps of hypothesis testing to analyze the following data (p<.01).

Attention Ratings (1=no attention- 5=full attention)

The data set represents the number of movies that a sample of 20 people watched in a year.

121 148 94 142 170 88 221 106 18 67 149 28 60 101 134 168 92 154 53 66

a.) construct a frequency distribution for the data set using six classes. Include class limits, midpoints, frequencies, relative frequencies, and cumulative frequencies. b.) Display the data using a frequency histogram (Must use EXCEL) c.) Describe the shape of the distribution as symmetric, uniform, skewed left, skewed right or none of these and give an interpretation of this data.

9.9. Is gender independent of education level? A random sample of people was surveyed and

each person was asked to report the highest education level they obtained. Perform a hypothesis

test. Include all 5 steps.

10.9. Compute and interpret the correlation coefficient for the following grades of 6 students

selected at random.

1. The primary rule of subject selection for experimental designs is the comparability of experimental and control groups. Ideally, the control group would be identical to the experimental group if it had not been exposed to the experimental stimulus. Therefore, the experimental and control groups should be as similar as possible. Probability sampling, randomization, and matching are several different methods for achieving this similarity.

One technique for ensuring an appropriate control group is the process of selecting multiple samples from a population using a method that is subject to chance rather than the bias of the experimenter and then assigning each sample to either an experimental or a control group. This technique is called A.PROBABILITY SAMPLING B. RANDOMIZATION

C. MATCHING

2. Nikhil is interested in finding out whether reading a comic strip about euthanasia will change people’s opinions on the subject. Nikhil decides to recruit a group of subjects and then divide the group into subgroups of older and younger students of each ethnicity. He then assigns half of each subgroup to be part of the experimental group and half to the control group, so that the experimental and control groups have the same makeup in terms of age and ethnicity. Nikhil administers a pretest to everyone to measure their opinions about euthanasia. Then the experimental group is asked to read the comic strip and the control group is not. Finally, Nikhil administers a posttest to everyone to see if their opinions about euthanasia have changed.

Which technique is Nikhil employing to ensure that the experimental and control groups are equivalent? A. Matching B. Randomization C. Probability sampling

3. The three different techniques have different advantages and disadvantages. In which of the following ways is randomization a better choice than matching? Check all that apply.

A. You do not necessarily know in advance which variables will be the most relevant for the study.

B.Randomization allows for conscious stratification.

C. Most of the statistics used to analyze the results of experiments assume randomization.

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.