Without replacement, what is the probability that

a) first card drawn is a jack, and the second card drawn is a queen

b) both cards drawn are red

When you have heard about probability, where did you think the estimations of likelihood came from?

How we are able to use the normal curve to make probability estimations?

Describe the utility of z scores in any simple analysis of data.?

2. You completed the study described above to determine the extent of anxiety symptoms in students at BMCC (random sample of 1,000 students). You also collected data on demographic variables. You sent out 1,000 surveys and got back 500.

a. What is the n? _____________

b. On your survey, 350 students were female. Construct a frequency distribution table for sex and create the appropriate graph to display the results.
What kind of variable is sex? _________________________

c. Your measure of anxiety symptoms can range from 0 to 20, where a higher number indicates more symptoms. Your measure had a mean of 7.2 with a standard deviation of 2.3. The median was 6, Q1 was 3 and Q3 was 10. The responses on this variable in your sample ranged from 0 to 19.
What kind of variable is this? _____________________
Test for outliers using this information. Which measures should you use for your descriptive statistics, the mean and standard deviation or the median and IQR?
Create a box whisker plot using this information.

d. You decide to split up your data by sex.
For women, minimum = 0, Q1 = 5, median = 8, Q3 = 11, maximum = 19.
Formen,minimum=0,Q1 =2,median=5,Q3 =8,maximum=15.
Create side-by-side box-whisker plots. Can you tell if there are differences between sexes? Explain.

e. You decide to create groupings for this variable based on the severity of symptoms. Anything below a score of 6 is “normal”, between 7 and 10 is “at risk” and anything above 10 is “likely anxiety.” In your sample, 283 participants fall into the “normal” group, 134 fall into the “at risk” group, while the rest are in the “likely anxiety” group. Please create a frequency distribution table and the appropriate graph to display the results.
What kind of variable is this? ________________

Below are the number of hours spent exercising:

1. How many participants were there in the study?

2. What percentage of the sample exercised 4 or more hours?

3. Report the following regarding the number of hours spent exercising, calculating by hand or using the Excel sheet provided to you.

Mean:
Median:
Mode:

Range:

Variance:

4. Which descriptive statistics from your output would you NOT report for hours spent exercising? Why not?

5. Write a few sentences describing the data (using APA formatting). This interpretation should not include only the numbers, but rather what the numbers tell you about the data.

6. Create a histogram for the hours spent exercising. You can do this by hand or via computer. If you do it by hand simply take a picture and upload it along with your assignment.

7. If you add 4 points to each exercise score, what will the mean and standard deviation be for this variable

Hint: You should not have to recalculate from the raw data to answer questions 7 & 8

8. If you subtract point from each exercise score, what will the mean and standard deviation be for this variable?

9. Give one example of data for each of the following and explain why?

a. When the median is more appropriate to use than the mean?

b. When the mean is more appropriate to use than the median?

c. When you would expect high variability?

d. When you would expect low variability?

10. When describing nominal data, which measure of central tendency is appropriate?

11. Why do we subtract 1 from the number of scores when calculating variance and standard deviation?

12. Describe how would you calculate standard deviation if you know variance?

1. A random variable is known to be normally distributed with the parameters shown below. Complete parts a and b.

μ=8.1and σ equals=0.70

a. Determine the value of x such that the probability of a value from this distribution exceeding x is at most 0.05.

b. Referring to your answer in part​ a, what must the population mean be changed to if the probability of exceeding the value of x found in part a is reduced from 0.20 to 0.10​?

2. A randomly selected value from a normal distribution is found to be 1.7 standard deviations above its mean.

a. What is the probability that a randomly selected value from the distribution will be greater than 1.7 standard deviations above the​ mean?

b. What is the probability that a randomly selected value from the distribution will be less than 1.7 standard deviations from the​ mean?

3. Assume that a random variable is normally distributed with a mean of 1,500 and a variance of 387.

a. What is the probability that a randomly selected value will be greater than 1563?

4. A random variable is normally distributed with a mean of 45 and a standard deviation of 55. If an observation is randomly selected from the​ distribution,

a. What value will be exceeded 10​% of the​ time?

b. What value will be exceeded 80​% of the​ time?

c. Determine two values of which the smaller has 15​% of the values below it and the larger has 15​% of the values above it.

d. What value will 20​% of the observations be​ below?

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 56 and estimated standard deviation σ = 48. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to three decimal places.)

(b) What is the probability that x < 40? (Round your answer to three decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to three decimal places.)

(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to three decimal places.)

A weight-lifting coach wanted to know whether weight-lifters can change their strength by taking a certain supplement. To answer this question, the coach randomly selected 8 athletes and gave them a strength test using a bench press. Thirty days later, after regular training using the supplement, they were tested again. The results were listed below. A test was conducted to determine whether weight-lifters can change their strength by taking a certain supplement. Assume the populations are normally distributed.

Athlete 1 2 3 4 5 6 7 8 Mean SD

Before 215 240 188 212 275 260 225 200 226.88 29.72

After 225 245 188 210 282 275 230 195 231.25 34.55

Difference -10 -5 0 2 -7 -15 -5 5 -4.38 6.55

1. What is the null hypothesis for this test?

2. What is the value of the standardized test statistic?

3. The p-value was 0.05. Suppose this test was conducted at α = 0.01. What can you conclude?

a. There is insufficient evidence to conclude that weight-lifters can change their strength by taking a certain supplement.

b. There is sufficient evidence to conclude that weight-lifters can change their strength by taking a certain supplement.

c. None of the above; this test is invalid.

4. Suppose the coach had incorrectly performed a two-sample t-test. In comparison to the correct analysis, which of the following regarding the test statistic would be true?

a. The test statistic is closer to 0

b. The test statistic is farther from 0

c. The test statistic does not change.

Find the relative frequency for the class with lower class limit 19

Relative Frequency = %

Give your answer as a percent, rounded to two decimal places

A Frequency Distribution Table using data
This list of 16 random numbers has been sorted:

Fill in this table with the frequencies as whole numbers and the relative frequencies as decimals with 4 decimal places for the relative frequencies. Remember: relative frequencies are between 0.0 and 1.0

(This problem does not accept fractions.)

Complete the table.

In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

Please round your answer to 4 decimal places for the Relative Frequency if possible.

What percent of students take exactly one courses? %

50 part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

a. Complete the table.

b. What percent of students take exactly two courses? %

70 adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below:

a. Complete the table (Use 4 decimal places when applicable)

b. What is the cumulative relative frequency for flossing 1 time per week? %

1. Find the GPA of the following grades.

A student received the following grades.

C     in Math 120   worth 4 credits.

B      in English 125 and worth 3 credits

A in Chem 102 and worth 5 credits.

2. According to Empirical Rule, the mean is 35 and the standard deviation is 3.

1. 68 % of the data lie between what values.
2. 95% of the data lie between what values
3. 99.7 % of the data lie between what values

4. Given the following data. Find the mean, variance , standard deviation of the population.

X     ( x -   µ )    (x - µ )²

2

5

6

Study Time and Exam Score

An elementary statistics instructor is interested in determining how well the amount of time students spend studying for her class predicts their results on exam. The instructor asks her students to keep track of the number of hours they spent working on their statistics course between the first and second exam (including in class time, tutoring time, computer time, etc.) She then recorded their score on the second exam and the results are shown below.

(A) Name the explanatory (predictor) and response variables for this analysis.

(B) What is the slope of the regression line? Interpret this value in context.

(C) What is the y-intercept of the regression line? Interpret this value in context.

(D) Determine the regression line.

(E) Use the equation of the regression line to predict a student's score when they study:

10 hours _____

20 hours _____

30 hours ____

(F) What is the residual for a person that studies 10 hours?

(G) What is the value of the correlation coefficient? Interpret this value.

For each question, write out the null and alternate hypotheses numerically. Give the test statistic and p-value. Write out the equation of the test statistic but you do not have to evaluate it by hand. Then conclude with whether you reject or fail to reject the null hypothesis.

Chapter 9

1. (Question 98.) Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

2. (Question 100.) According to an article in Bloomberg Businessweek, New York City's most recent adult smoking rate is 14%. Suppose that a survey is conducted to determine this year’s rate. Nine out of 70 randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased.

Chapter 10

3. (Question 124). A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. The population standard deviations are two pounds and three pounds, respectively. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. Conduct a hypothesis test to determine if there is a difference in these two diets

4. (Question 13) Lesley E. Tan investigated the relationship between left-handedness vs. right-handedness and motor competence in preschool children. Random samples of 41 left-handed preschool children and 41 right-handed preschool children were given several tests of motor skills to determine if there is evidence of a difference between the children based on this experiment. The experiment produced the means and standard deviations shown Table 10.36. Conduct a hypothesis test to determine if there is a difference in motor competence

Left-handed Right-handed

Sample size                                        41                    41

Sample mean                                     97.5                 98.1

Sample St. Dev.                                 17.5                 19.2

The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 48 male consumers was $135.67, and the average expenditure in a sample survey of 34 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $40, and the standard deviation for female consumers is assumed to be $23.

1. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?
   
2. At 99% confidence, what is the margin of error (to 2 decimals)?
   
3. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.
   (  ,   )

(Round all intermediate calculations to at least 4 decimal places.) Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. Linear Quadratic Cubic Intercept 25.97 20.73 16.20 x 0.47 2.82 6.43 x2 NA −0.20 −0.92 x3 NA NA 0.04 R2 0.060 0.138 0.163 Adjusted R2 0.035 0.091 0.093 pictureClick here for the Excel Data File a. Predict y for x = 3 and 5 with each of the estimated models. (Round your answers to 2 decimal places.) Linear yˆ Quadratic yˆ Cubic yˆ x = 3 x = 5 b. Select the most appropriate model. Cubic model Quadratic model Linear model

EACH STUDENT IN YOUR CLASS SHOULD HAVE GOTTEN A SLIGHTLY DIFFERENT CONFIDENCE INTERVAL. WHAT PROPORTION OF THOSE INTERVALS WOULD YOU EXPECT TO CAPTURE THE TRUE POPULATION MEAN? WHY? IF YOU ARE WORKING IN THIS LAB IN A CLASSROOM, COLLECT DATA ON THE INTERVALS CREATED BY OTHER STUDENTS IN THE CLASS AND CALCULATE THE PROPORTION OF INTERVALS THAT CAPTURE THE TRUE POPULATION MEAN.

Subject: Statistics

Please show complete work for the multiple-choice questions below

1. If the mean and median are equal, you know that the:
a. distribution is symmetrical
b. distribution is skewed
c. distribution is normal
d. mode is equal to the median

2. The mean, median and mode are all measures of:
a. the midpoint of the distribution
b. the most common score
c. percentile ranks
d. variability

3. Which of the following characterizes the mean?
a. The sum of all the measurements divided by the number of measurements.
b. The point in a distribution about which the summed deviations equal zero.
c. The point in a distribution about which the sum of the squared deviations
is minimal.
d. All of the above.

4. Which statistic does not belong with the others?
a. range
b. mean
c. variance
d. standard deviation

5. Which of the following samples exhibits the least variability?
a. 2,4,6,8,l0,l2
b. 2,2,3,ll,l2,l2
c. 2,3,4,l0,ll,l2
d. 2,6,7,7,8,l2