Stat 353 Final Exam

Directions:

• The exam consists of 10 questions, each assigned a value of 15 points.
• The total time allocated for completing the exam is 2 hours and 15 minutes.
• In the absence of a specified significance level for a hypothesis test, use \(\alpha=0.05\) as the default.

Question 1:

A manufacturing company claims that the average time to assemble a product is 22 minutes. To verify this claim, a sample of assembly times (in minutes) is collected:

28, 32, 29, 31, 30, 28, 33, 30, 31, 29, 30, 32, 31, 30, 29, 32, 30, 33, 29, 31, 30, 32, 29, 31, 30

Perform a test to determine if the mean assembly time significantly differs from the company’s claim.

How many of the following are correct?

• The null hypothesis is \(\mu \ne 22\)
• The test statistic value is 29.70 in two decimal places.
• The p-value is less than 0.01.
• Reject the null hypothesis.

Question 2:

In a survey of 500 customers, the company wants to assess if the proportion of satisfied customers with a new product (out of 500) is significantly different from the expected satisfaction rate of 25%.

• Total customers surveyed: 500
• Customers satisfied: 120

Conduct an appropriate test at a significance level of 0.05.

How many of the following are correct?

• The null hypothesis is \(p \ne 0.25\)
• The p-value is less than 0.05.
• Reject the null hypothesis.

Question 3:

The education department is comparing the effectiveness of two teaching methods, A and B. Students are randomly assigned to each method, and their scores are collected:

• Method A: 75, 80, 85, 78, 88, 82, 79, 81, 86, 90
• Method B: 70, 85, 88, 76, 92, 80, 77, 82, 84, 89

Conduct a test to determine if there is a significant difference in the mean scores achieved by students using each method.

How many of the following are correct?

• The null hypothesis is \(\mu_A = \mu_B\)
• The p-value is greater than 0.50.
• Don’t reject the null hypothesis.

Question 4:

A quality control manager is comparing the defect rates of two assembly lines, X and Y.

• Line X: 400 units, 20 defects
• Line Y: 450 units, 40 defects

Conduct a test to assess if there is a significant difference in the proportion of defective products between the two lines.

How many of the following are correct?

• The null hypothesis is \(p_1 \ne p_2\)
• The p-value is less than 0.03.
• Reject the null hypothesis.

Question 5:

A manufacturing company produces steel rods using materials A, B, and C. Tensile strength measurements (in arbitrary units) are collected:

• Material A: 45, 48, 41, 43, 50, 42, 44, 47, 42, 40, 49, 46, 43, 41, 48
• Material B: 46, 49, 43, 45, 50, 44, 48, 46, 42, 45, 47, 43, 45, 49, 50
• Material C: 47, 45, 42, 49, 46, 50, 48, 44, 41, 46, 49, 42, 45, 47, 48

Conduct a one-way ANOVA to determine if there is a significant difference in the mean tensile strength across the three materials.

How many of the following are correct?

• The alternative hypothesis is all population means are different.
• The test statistic value is 1.26 in two decimal places.
• The p-value is less than 0.10.
• Reject the null hypothesis.

Question 6:

Engineers are exploring the relationship between the diameter (x) of steel rods and their tensile strength (y).

• Diameter (x): 11.8, 11.9, 11.5, 11.7, 11.9, 11.6, 11.7, 11.8, 11.6, 11.5, 11.9, 11.8, 11.7, 11.6, 11.5, 11.8, 11.9, 11.6, 11.7, 11.8
• Tensile Strength (y): 45, 48, 41, 43, 50, 42, 44, 47, 42, 40, 49, 46, 43, 41, 48, 52, 45, 43, 46, 49

Conduct a simple linear regression analysis.

How many of the following are correct?

• The regression equation is \(y=-151.60+16.80x\).
• the variable \(x\) is significant.
• For each one unit increase in \(x\), \(y\) increases by 16.80, on average.
• Using the model obtained, the tensile strength of a steel rod that has a diameter of 11.6 is predicted to be 43.28.

Question 7:

Which of the following is not a typical use for a p-chart?

1. Monitoring the proportion of defective items in a batch
2. Tracking the percentage of products that pass inspection
3. Monitoring the proportion of machines running in a factory
4. Controlling the mean of a continuous measurement

Question 8:

A quality control engineer is monitoring the proportion of defective items in a manufacturing process. The engineer collects 20 samples, each of size 50 items. The number of defective items in each sample is as follows:

\[2,3,4,1,2,3,5,2,3,1,2,3,4,2,3,1,5,4,2,3\] The center line of the \(p\)-chart is at

1. 0.045
2. 0.050
3. 0.055
4. 0.060

Question 9:

The company is interested in understanding if the distribution of defective products across different categories (X, Y, Z) matches the expected distribution:

• Category X: 30%
• Category Y: 40%
• Category Z: 30%

The numbers of defective products across different categories (X, Y, Z) are

• Category X: 40
• Category Y: 55
• Category Z: 55

Conduct a test to determine if the observed defect distribution differs significantly from the expected distribution.

How many of the following are correct?

• The null hypothesis is that the data is consistent with the proportions provided.
• The test statistic value is 3.19 in two decimal places.
• The p-value is less than 0.05.
• Reject the null hypothesis.

Question 10:

Researchers want to investigate whether there is a relationship between the type of material used (A, B, C) and the presence of surface defects (Yes/No).

• Material Type (A, B, C): A, A, B, B, C, C, A, A, B, B, C, C, A, A, B, B, C, C, A, A, B, B, C, C
• Surface Defects (Yes/No): Yes, No, Yes, No, Yes, No, Yes, No, Yes, No, Yes, No, Yes, No, Yes, No, Yes, No, Yes, No, Yes, No, Yes, No

Conduct an appropriate hypothesis test.

The test method can be a

1. \(t\) test
2. \(F\) test
3. \(\chi^2\) test
4. None of these