An experimenter flips a coin 100 times and gets 62 heads. We wish to test the claim that the coin is fair (i.e. a coin is fair if a heads shows up 50% of the time). Test if the coin is fair or unfair at a 0.05 level of significance. Calculate the z test statistic for this study. Enter as a number, round to 2 decimal places.

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.77.

(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 16 specimens from the seam was 4.85. (Round your answers to two decimal places.)

  ,

(b) Compute a 98% CI for true average porosity of another seam based on 12 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)

  ,

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.49? (Round your answer up to the nearest whole number.)
specimens

(d) What sample size is necessary to estimate true average porosity to within 0.23 with 99% confidence? (Round your answer up to the nearest whole number.)
specimens

1. A software company is trying to use Bayes Theorem and other rules of probability to develop an algorithm that can effectively filter out spam emails. The company’s software developers carefully examined a random sample of 20,000 emails received by its employees and found out that 4,400 of the emails were spam. A closer look at the spam emails revealed that 1,100 of them contained the word ‘free’ in the subject line. On the other hand, only 780 of the non-spam emails had the word ‘free’ in their subject line. Please answer the following questions based on the given information.

a. What is the probability that a random email will be a spam and will not contain the word ‘free’ in its subject line? Please show your work.            

b. If the word ‘free’ does not appear in the subject line of an email, what is the probability that the email is not a spam? Please show work.                  [2 points]

1. c. What is the probability that a random email will be neither a spam and nor will contain the word ‘free’ in its subject line? Please show your work.         [2 points]                                
   1. d. Are an email being a spam and its subject line containing the word ‘free’ independent events? Please show how you arrived at your answer.      [1 point]

7. A consumer psychologist wishes to determine whether playing music increases sales at a local department store. To this end, the psychologist has the owner play either no music, soft rock, or classical music and notes the sales for 21 people (7 in each) under these three conditions. The dependent variable is dollars spent per shopper. The table below contains the data from this experiment. Perform a one-way ANOVA to address the consumer psychologist’s research question.

Calculate the group means and grand mean and put your answers in the spaces provided.

No Music_____ Soft Rock_____ Classical_____

Grand Mean_____

8. Please write the null hypothesis for this analysis in both equation and written form.

9. Please write the research hypothesis for this analysis in both equation and written form.

10. Fill in the source table below based on your calculations.

11. Researchers were interested in how age is related to alcohol consumption. As such, they conducted a study dividing 150 subjects into 5 age groups and looking for average differences in alcohol consumption measured as drinking days per month. Sum of squares total is 1341. The authors of the study reported effect size eta-squared of .51. Find the value of the F-ratio.

1)      A personal director is interested in studying the relationship (if any) between age and salary. Sixteen employees are randomly selected and their age and salary are recorded.

a)      Plot the data points on a scatterplot.

b)      Determine the correlation coefficient   

c)       Describe the relationship indicated by the correlation coefficient and the scatterplot.

d)      If there is a linear relationship, find the equation of the line of regression

e)      Graph the line of regression on the same axes where you constructed the scatterplot in (a) above

f)       Use either your line of regression or the equation of the line of regression to predict salaries for Age = 50 and Age = 70.

F6: In a waiting line situation, arrivals occur around the clock at a rate of six per day, and the service occurs at one every three hours. Assume the Poisson and exponential distributions.

Please show your work

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days.

1. State the null and alternative hypotheses.
2. t-test or z-test?
3. Calculate test statistic
4. Using a critical value, test the null hypothesis at the 5% level of significance. State conclusion.

In the past the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 25 employees was selected. The average age in the sample was 45 years with a standard deviation of 5 years. Assume the distribution of the population is normal. Let a = .05.

1. State the null and the alternative hypotheses.
2. z-test or t-test?
3. Test to determine whether or not the mean age of all employees is significantly more than 40 years (You may pick which method). State conclusion in a full sentence.

A testing center at the university wants to compare the average test taking time of undergraduate students on a standardized entrance exam to graduate school. Four departments are selected, and from each department, 25 students are randomly sampled (100 students total). The center then checks for test taking time (in minutes), and compares the average test taking time of students using ANOVA. Complete the following one-factor ANOVA summary table using alpha = .05. Based on the results, do students in different departments have different departments have different test taking times?

A kinesiologist wanted to investigate the effect of temperature and humidity on human performance. He found 28 college students and randomly assigned them to four different conditions, during which they were to walk at their normal pace on a treadmill for 60 minutes. He measured how far, in miles, they walked. The conditions varied in temperature (normal temperature/high temperature) and humidity (normal humidity/high humidity). The data are presented below, and SSwithin = 1.58. Do all hypothesis testing steps and compute effect sizes. Note that T = Σx.  

Normal Temperature, Normal Humidity

n = 7

M = 3.00

T = 21

Normal Temperature, High Humidity

n = 7

M = 2.80

T = 19.60

High Temperature, Normal Humidity

n = 7

M = 2.80

T = 19.60

High Temperature, High Humidity

n = 7

M = 2.00

T = 14

A random sample of Midsize Sedans’ Miles per Gallon (mpg) were recorded and the                   data is listed below. Assume the miles per gallon are normally distributed:

24.6      30.2      29.9      33.1      26.7

28.5      31.6      36.3      24.4      28.7

1. Calculate the mean (1 pt):

2. Calculate the standard deviation (1 pt):

3. Construct a 90% confidence interval for population mean (4 pts):

4. Construct a 95% confidence interval for population standard deviation (4 pts):

Research into the relationship between hours of study and grades shows widely different conclusions. A recent survey of graduates who wrote the Graduate Management Admissions Test (GMAT) had the following results.​

a) Run the regression analysis in Excel on this data. Include your output with your answer. (Note: You may calculate by hand if you prefer).

b) What is the regression equation for this relationship?

c) Use the regression equation to predict the average score for each category of hours studied.

d) Plot the original data and the regression line on a scatter gram. (You may use Excel).

e) How accurate is this regression at predicting GMAT scores based on hours studied? Explain.

f) Use the t statistic to determine whether the Correlation Coefficient is “significant” at the 95% confidence level.

A study looked at number of cavity children per 100 in 18 North American cites before and after public water fluoridation projects. The following table lists the data.

a. Please test whether there is a significant change in number of cavity children per 100 after and before public water fluoridation. Make sure you include all the five steps in the hypothesis testing questions.

b. What is the 95% confidence interval for the change?

29-34. Matching – fill in the blank with the correct response from A-E below:

A). ANOVA B). Pearson’s r C). Chi Square D). Multiple Regression E). t-test

29. ______ This parametric test analyzes the means between groups, to determine if the group means differ significantly from one another. This test helps reduce Type I errors, and is closely related to the t-test.

30. ______ This is a parametric test used when two measures are taken on one sample, or when measures are obtained from two closely related sample groups, to see if there is a difference between the two groups.

31. _______ This parametric test can be used to test the significance of the correlation coefficient between two variables measured at the interval or ratio level.

32. _______ This parametric test calculates an F statistic, which provides information about variation between group means.

33. ______A non-parametric test that is useful for identifying differences between groups, by analyzing nominal or ordinal data such as age and gender.

34. _______A parametric test used to determine the relationship among several independent variables on one dependent variable, by measuring ratios or interval data

Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow: Month Machine Hours Electricity Costs January 3,000 $ 18,650 February 3,400 $ 21,500 March 2,400 $ 13,750 April 3,600 $ 23,500 May 4,300 $ 28,500 June 3,800 $ 22,500 July 4,600 $ 25,000 August 4,000 $ 23,000 September 2,500 $ 16,000 October 4,200 $ 26,500 November 5,600 $ 31,500 December 5,200 $ 28,000 Summary Output Regression Statistics Multiple R 0.952 R Square 0.906 Adjusted R2 0.897 Standard Error 1,676.51 Observations 12.00 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3,639.33 2,048.60 1.78 0.11 (925.25) 8,203.90 Machine Hours 5.04 0.51 9.83 0.00 3.89 6.18 Based on the results of the regression analysis, the estimate of electricity costs in a month with 2,700 machine hours would be: (Round to the nearest whole dollar. Your answer may be different by a few dollars due to rounding of the regression coefficients. Choose the answer closest to your calculation.)

What sport games does it have 8 or more than 8 teams in one group where a round robin game sequence takes place? (that is, the teams play against each other once or more than once)