Instructions: Answer all questions. Show your work where applicable.

Question 1: One-Sample Hypothesis Testing (5 points)

A company claims that their new software reduces the average response time for customer inquiries to less than 15 minutes. You collect a random sample of 20 customer inquiries and record the response times (in minutes) as follows:

14,15,12,14,16,13,15,13,14,15,12,16,14,15,13,15,12,14,15,13

Perform a hypothesis test to determine if there’s enough evidence to support the company’s claim at a significance level of 0.05.

Question 2: Two-Sample Hypothesis Testing (10 points)

A manufacturer is interested in whether two different machines produce parts with different mean weights. They collect data from 30 parts produced on Machine A and 35 parts produced on Machine B. The sample weights (in grams) for the two machines are as follows:

Machine A:

12,13,12,11,14,12,13,14,11,12,13,14,11,12,13,14,12,13,11,14,12,13,12,14,11,12,13,14,11,12

Machine B:

14,11,13,14,11,13,14,12,13,12,13,14,11,12,13,14,11,13,12,13,14,12,13,11,12,13,14,12,13,14,11,12,13,14

Perform a hypothesis test to determine if the mean weights of the two machines are significantly different at a significance level of 0.05.

Question 3: Confidence Interval for Proportion (5 points)

In a survey of 500 customers, 160 reported that they use the product regularly. Calculate a 95% confidence interval for the proportion of customers who use the product regularly.

Question 4: Chi-Square Test for Independence (10 points)

A researcher is examining the relationship between the preferred type of smartphone (iPhone, Android, Other) and age group (18-24, 25-34, 35-44). They collect data from a sample of 300 individuals, and the contingency table of the data is as follows:

##        smartphone
## Age     Android iPhone Other
##   18-24      60     40    10
##   25-34      30     50    20
##   35-34      40     20    10

Perform a chi-square test for independence to determine if there’s a significant relationship between smartphone preference and age group at a significance level of 0.05.

Question 5: Regression Analysis (10 points)

A researcher is interested in the relationship between the number of hours of study (x) and the exam scores (y) of 25 students. The data for the study hours (x) and exam scores (y) are as follows:

Study Hours (x):

10,15,8,12,18,7,14,17,10,11,16,9,12,13,8,19,15,14,11,9,16,17,13,10,18

Exam Scores (y):

75,82,68,76,88,66,80,85,70,72,84,69,78,79,68,89,83,81,73,70,86,84,76,71,87

Fit a simple linear regression model and provide the complete regression equation. Interpret the coefficients.

Question 6: Control Chart for Quality Control (10 points)

In a manufacturing plant, you collect data on the diameter of steel washers produced over 30 production runs, with each run consisting of 5 washers. The individual diameters (in millimeters) for each production run are as follows:

Production Run 1:

8.9,9.1,9.0,9.2,9.0

Production Run 2:

8.7,9.2,8.9,9.1,9.0

Production Run 3:

9.1,9.0,8.8,8.9,9.2

Production Run 4:

8.9,9.1,9.0,9.2,9.0

Production Run 5:

8.7,9.2,8.9,9.1,9.0

Production Run 6:

9.1,9.0,8.8,8.9,9.2

Production Run 7:

8.9,9.1,9.0,9.2,9.0

Production Run 8:

8.7,9.2,8.9,9.1,9.0

Production Run 9:

9.1,9.0,8.8,8.9,9.2

Production Run 10:

8.9,9.1,9.0,9.2,9.0

Production Run 11:

8.7,9.2,8.9,9.1,9.0

Production Run 12:

9.1,9.0,8.8,8.9,9.2

Production Run 13:

8.9,9.1,9.0,9.2,9.0

Production Run 14:

8.7,9.2,8.9,9.1,9.0

Production Run 15:

9.1,9.0,8.8,8.9,9.2

Production Run 16:

8.9,9.1,9.0,9.2,9.0

Production Run 17:

8.7,9.2,8.9,9.1,9.0

Create an X-bar control chart for the diameter of steel washers using the provided data. Include control limits and interpret the chart.

Question 7: Goodness of Fit Test (5 points)

A grocery store claims that the distribution of customer payment methods is 60% credit card, 30% cash, and 10% check. You observe the payment methods of 200 customers and find that 110 use credit cards, 70 pay in cash, and 20 pay by check. Perform a chi-square goodness-of-fit test to determine if the observed payment method distribution differs significantly from the store’s claim at a significance level of 0.05.

Question 8: Paired Sample Hypothesis Testing (5 points)

A training program claims that participants will increase their typing speed after completing the program. You collect data from 20 participants, recording their typing speeds before and after the program. The differences in typing speed (after - before) are as follows:

10,15,8,12,17,11,14,19,13,10,12,9,15,16,7,18,14,13,11,12

Perform a hypothesis test to determine if there’s enough evidence to support the training program’s claim at a significance level of 0.05.