Which of the following is the complete definition of the simple linear regression model?

Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 40 women athletes at the school showed that 22 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance.

(a) State the null and alternate hypotheses. H0: p < 0.67; H1: p = 0.67 H0: p = 0.67; H1: p < 0.67 H0: p = 0.67; H1: p ≠ 0.67 H0: p = 0.67; H1: p > 0.67

(b) What sampling distribution will you use? The standard normal, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5. The Student's t, since np > 5 and nq > 5. The Student's t, since np < 5 and nq < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find the P-value of the test statistic. (Round your answer to four decimal places.) and Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the true proportion of women athletes who graduate is less than 0.67. There is insufficient evidence at the 0.01 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

Below is the data for a personality questionnaire measuring conscientiousness. These data were taken from a random sample of 25 undergraduate psychology majors. In the general population, scores on this questionnaire are normally distributed with a mean (μ) of 60. You hypothesize that this sample is not representative of the general population. Specifically, you hypothesize that psychology students form a distinct sub-population, with DIFFERENT conscientiousness, relative to the general population. That is, it would be equally interesting to find out they have higher or lower conscientiousness. Conduct a one-sample t-test by answering the following questions.

Data: N = 25, xbar (sample mean) = 65.12, S_x = 10.17

  a. State the null and alternative hypotheses.

  b. Are you going to be using a one- or two-tailed test? Explain the reason for your choice.

  c. What are the degrees of freedom for this t-test? Find the corresponding critical t-value for Type I error rate (alpha) of α = 0.05?

d. Calculate your observed t-statistic.

e. Compare your observed t-statistic to the critical t-value(s). What do you conclude regarding the null hypothesis?

f. Calculate and interpret follow-up 95% Confidence interval

g. Calculate and interpret the standardized effect size (Cohen's d).

h. What do you conclude about your research question (use your own words, in everyday language)

It may be that sunshine has a unique effect on learning statistics. Previous research has been in disagreement, with some studies showing that sunshine increases amount learned whereas others show sunshine has detrimental effects on learning. You would like to determine for yourself whether or not sunshine makes a DIFFERENCE on statistics learning. Let's assume you take five statistics students and give them a lesson on a sunny day, and then take a completely different and unrelated five students and give them the same lesson on a rainy day. These are their results for a quiz on their lesson:

Sunny Day Students:

• Student 1: 9.8
• Student 2: 6.7
• Student 3: 7.2
• Student 4: 8.2
• Student 5: 5.1

xbar₁ = 7.4

Rainy Day Students:

• Student 6: 8.2
• Student 7: 6.7
• Student 8: 6.8
• Student 9: 9.7
• Student 10: 7.1

xbar₂ = 7.7

a. State the null and alternative hypotheses.

b. What are the degrees of freedom for this t-test? Find the corresponding critical t-value(s) for Type I error rate (alpha) of α = 0.05?

c. Calculate your observed t-statistic (hint: you will need to calculate the standard deviations of both groups first).

d. Compare your observed t-statistic to the critical t-value. What do you conclude regarding the null hypothesis?

e. Calculate and interpret the 95% Confidence interval.

f. Calculate and interpret the standardized effect size (Cohen's d).

g. What do you conclude about your research question (use your own words, in everyday language).

Chapter 11 Estimation and Confidence Intervals - Please answer 2-4

Practice 2) Estimation for the one-sample t Test

In chapter 9, we computed a one-sample t test examining the social functioning of relatives of individuals with OCD compared to the general healthy population.

In 18 participants, M = 62.00; SD = 20.94

Find the 95% CI for these data

Practice 3) Estimation for the two-independent-sample t test

In chapter 9, we tested the mean difference of calorie consumption between two independent groups given the same buffet: One group was instructed to eat fast, and another group was instructed to eat slowly. In a sample of 12 participants, we recorded M=600 in Grout Eating Slowly and M=650 in Group Eating Fast with an estimated standard error for the difference of S_M1-M2 = 82.66. Here we will find the 95% confidence interval for these data.

Practice 4) Estimation for the Related-Sample t Test

In chapter 10, we tested if teacher supervision influences the time that elementary school children read. The difference in time spent reading in the presence versus absence of a teacher was M_D=15 (n=8); the estimated standard error for the difference was S_MD=5.35. Here we will find the 95% confidence interval for these data.

A dept. Store marketing study claims 40% of customers prefer Calvin Klein, 30% prefer Tommy Hilfiger, 20% prefer Ralph Lauren and 10% prefer other. A survey of 500 customers finds the following: 175 prefer Calvin Klein, 150 prefer Tommy Hilfiger, 150 Prefer Ralph Lauren and 25 prefer other.

Test the goodness of-fit of the marketing study's model using alpha =.05

A factory has in it five machines, A, B, C, D, and E that produce Smart Pencils.

Machine A produces 5 % of the factory's output with a 2 % defective rate.

Machine B produces 10 % of the factory's output with a 3 % defective rate.

Machine C produces 25 % of the factory's output with a 4 % defective rate.

Machine D produces 3 0% of the factory's output with a 5 % defective rate.

Machine E produces 3 0% of the factory's output with a 6 % defective rate.

1.

A pencil is selected at random and found to be defective. What is the probability it was produced by Machine A?

2.

A pencil is selected at random and found to be defective.

What is the probability it was produced by Machine A or E?

Determine the minimum sample size required when you want to be 90​% confident that the sample mean is within one unit of the population mean and sigma=10.8. Assume the population is normally distributed.

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

From a random sample of 45 business​ days, the mean closing price of a certain stock was ​$116.70. Assume the population standard deviation is ​$11.02. The​ 90% confidence interval is

Construct the indicated confidence interval for the population mean using the​ t-distribution. Assume the population is normally distributed.

c=0.99 x =14.2​, s= 0.73 ​, n=14

An educational psychologist studies the effect of frequent testing on retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below.

Frequent Quizzes Two Exams

n=20 n=20

M=73 M=68

a. If the first sample variance is s2 = 38 and the second sample has s2 = 42, do the data indicate that testing frequency has a significant effect on performance? Use a two-tailed test at the .05 level of significance. (Note: because the two sample are the same size, the pooled variance is simply the average of the two sample variances.)

b. If the first sample variance is s2 = 84 and the second sample has s2= 96, do the data indicate that testing frequency has a significant effect? Again, use a two-tailed test with x = .05.

c. Describe how the size of the variance effects the outcome of the hypothesis test.

Could you please give me step-by-step on how to solve this. Thank you!

I believe that the population proportion for 50% of the people who live in my neighborhood drive a mini van. I surveyed 40 people/houses in my neighborhood and found that only 19 drive mini vans. Use the significance level .10 to test the hypothesis.

Determine P(Z<-1.85). Report your answer to four decimal places.

QUESTION 11

1. A pharmacologist decided to test two common headache-tablets for their effectiveness: Tablet A 500mg and Tablet B 20 mg. The experiment was conducted as follows: A random patient that walked into the clinic and complained of a headache was given either tablet A, tablet B, or a placebo. After swallowing the tablet the patient was asked to stay in the clinic for an hour and afterwards to report whether the headache had disappeared, improved, or if the tablet had no effect (i.e. no improvement or even a worsening of the headache intensity). Use a 1% level of significance to test the claim that headache status is independent of headache relief tablet used.

   	Headache Disappeared	Headache Improved	No Change	Total
   Tablet A	70	20	15	105
   Tablet B	70	10	20	100
   Placebo	50	30	25	105
   Total	190	60	60	310

   
   Contingency Table: Headache 4
   Hypotheses:
   H₀: Headache status is independent of headache relief tablet used.
   H₁: Headache status is dependent on headache relief tablet used.
   
   Expected Values:
   Complete the 3x3 table of expected outcomes (round values to 3 decimal places).

   	Headache Disappeared	Headache Improved	No Change
   Tablet A	_____	20.323	______
   Tablet B	______	_______	19.355
   Placebo	64.355	________	_____

   
                                 
   Results:
   Calculate the  test statistic (use two decimal places).
   
   ________
   State the p-value (round answer to the nearest hundredth of a percent - i.e. 1.53%)

   p-value =________
   
   Conclusion:
   We_________ sufficient evidence to support the claim that patient headache status is dependent on which headache relief tablet was used (p_____ 0.01).
   (Use “have” or “lack” for the first blank and “<” or “>” for the second blank.)

1. Government standards limit the airborne amount of a known cancer causing gas. A company using a known cancer causing gas in its production process limits the exposure of its employees to the gas by shutting down production when the amount of the gas reaches 3 ppm with a standard deviation of 0.5 ppm.

1. (2) If you are the plant manager and you are told management wants as little down time as possible, would you choose a larger or a smaller value of alpha to test whether the amount of gas is dangerous? Explain.
2. (2) If you were an employee in the plant, would you want the choice of alpha to be larger or smaller? Explain.
3. (5) A random sample of 50 air specimens from various sensors in the plant produced a mean of 3.1 ppm. Is this sample data sufficient to shut down production? Use alpha = 0.01.
4. (2) Describe both Type I and Type II errors in the context of this problem.
5. (6) Calculate the probability of Type II error if in fact the true mean plant level if 3.1 ppm. Use alpha = 0.01.
6. (1) What is the value of the Power of the test in this case?

The values of y and their corresponding values of y are shown in the table below

A) Calculate the coefficient of correlation;

B) Calculate the coefficient of determination;

C) Obtain the regression coefficients and write the regression expression;

D) Provide your prediction of the dependent variable if the value of the independent variable is 4.