A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.
An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost of apartments based on the size of the apartment. Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx.
Apartments.xlsx
At the .05 level of significance determine if the correlation between rental cost and apartment size is significant.
Two independent samples of sizes n_{1} = 50 and n_{2} = 50 are randomly selected from two populations to test the difference between the population means, . The sampling distribution of the sample mean difference, is:
Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.
Patient
1
2
3
4
5
6
7
Before
158
189
202
353
416
426
441
After
284
214
101
227
290
176
290
Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?
You conduct a hypothesis test and you observe values for the sample mean and sample standard deviation when n = 25 that do not lead to the rejection of H_{0}. You calculate a p-value of 0.0667. What will happen to the p-value if you observe the same sample mean and standard deviation for a sample size larger than 25?
A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 90% confidence interval for the average days worked by employees in all payroll departments?
The number of ways to choose two representatives from a committee of 13 people is
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
A sport preference poll yielded the following data for men and women. Use a 5% significance level and test to determine if sport preference and gender are independent.
Sport Preferences of Men and Women
Basketball
Football
Soccer
Men
20
25
30
75
Women
18
12
15
45
38
37
45
120
What is the test value for this hypothesis test?
Answer: Round your answer to two decimal places.
What is the critical value for this hypothesis test?
Answer: Round your answer to two decimal places.
What is the conclusion for this hypothesis test? Choose one.
1. There is sufficient evidence to support the claim that one's sport preference is dependent on one's gender. 2. There is not sufficient evidence to support the claim that one's sport preference is dependent on one's gender.
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 8 unacceptable assemblies.
If you are interested in determining if there is sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies, what is/are the critical value you would use to conduct such a test of hypothesis?
Place your answer, rounded to 2 decimal places, in the blank. If there are two critical values, place only the positive value in the blank. For example, 2.34 would be a legitimate entry.
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam.
What score represents the 70th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry.
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
If a sample has 25 observations and a 99% confidence estimate for is needed, the appropriate value of the t-multiple required is . Place your answer, rounded to 3 decimal places, in the blank. For example, 3.456 would be an appropriate entry.
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.
Number of Products Purchased
Brands Purchased
Fewer
Same
More
Total
Same
10
14
24
48
Changed
262
82
8
352
Total
272
96
32
400
What is the probability that a consumer selected at random purchased fewer products than before? Place your answer, rounded to 4 decimal places, in the blank.
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
The ABC battery company claims that their batteries last 100 hours, on average. You decide to conduct a test to see if the company's claim is true. You believe that the mean life may be different from the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below.
Test of H_{0}: = 100 versus H_{1}: 100 Sample mean 98.5 Std error of mean 0.777
Assuming the life length of batteries is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, 0.234 would be a legitimate entry.
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:
= chocolate chosen
= strawberry chosen
= vanilla chosen
= ice cream on a cone
ice cream in a cup
Find the probability that the ice cream was strawberry flavor, given that it was sold in a cup.Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.