Groups of dolphins were systematically observed off the coast of Iceland near Keflavik in 1998. Each observation included the main activity of a dolphin group (Activity) and the time of day the group was observed (Time). The groups varied in size, with feeding or socialising groups usually including more dolphins than travelling groups, but no information about group size was included with the data. The observations are summarised in the following table: No. of groups, summarised by activity and time. Time Morning Noon or Afternoon Evening Activity Travelling 6 20 13 Feeding 28 4 56 Socialising 38 14 10

(a) In looking for an association between Activity and Time, which variable would be the predictor and which the response? Justify your answer.

(Is this correct),My answer is-

1. The predictor variable is the main activity of a dolphin group

         (Activity) and the response variable the time of day the group was

         observed (Time). The Activity of the dolphins decides what time of day

         it is.

(b) How strong is the evidence that dolphin activity typically varies during the day? Test at a 1% significance level.If you conclude that there is a relationship, describe it.

Does this look like I am on the right path?

(My answer)

1. H0: There is no association between Dolphin Activity and the Time of day.

H1: There is some association.

     Significance Level: α= 0.01

         The test requires for the sample to be randomly selected and all the

         expected observations to be ≥5.

(My question)-It says the dolphins are systematically observed(does that mean it is not a random sample?)

Assume that a certain batch of 200 castings contains 5 defectives. Calculate the probability that of three castings selected, exactly one will be defective. Answer: 0.0720 (Show work and reasoning!)

*

*****Complete #3 two ways*********

            i. Same as in Example above

            ii. using the Excel NORMDIST and NORMINV functions

                        demonstrated in the Prob Dist podcast

NOTE: Excel functions (just as the table) may not directly give the answer you are looking for, you must understand what they return and how to use it.

3. The average amount parents spent per child on back-to-school clothes in Fall 2019 was $635. Assume the standard deviation is $150 and the amount spent is normally distributed.

a. What is the probability that the amount spent on a randomly selected child is more than $800?

b. What is the probability that the amount spent on a randomly selected child is more than $500

c. 95% of the parents will spend more than what amount?

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