# The percent defective for parts produced by a manufacturing process

1.     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 percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives.

Determine a 95% confidence interval for the proportion defective for the process today.

Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer.

Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry.

2.     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 sample of 9 production managers with over 15 years of experience has an average salary of \$71,000 and a sample standard deviation of \$18,000.

Assuming that s = 18,000 is a reasonable estimate for what sample size would be needed to ensure that we could estimate the true mean salary of all production managers with more than 15 years experience within \$4200 if we wish to be 95% confident? Place your answer, as a whole number, in the blank. Do not use a dollar sign, a comma, or any other stray mark. For examples, 34 would be a legitimate entry.

3.     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 sample of 9 production managers with over 15 years of experience has an average salary of \$71,000 and a sample standard deviation of \$18,000.

Assuming that the salaries of production managers with over 15 years experience are normally distributed, you can be 95% confident that the mean salary for all production managers with at least 15 years of experience is between what two numbers.

Place your LOWER limit, rounded to a whole number, in the first blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 54321 would be a legitimate entry. . Place your UPPER limit, rounded to a whole number, in the second blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 65432 would be a legitimate entry.

4.     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.

After calculating the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (E) must be reduced to just 0.025. If the original calculation led to a sample size of 1000, the sample size will now have to be . Place your answer, as a whole number in the blank. For example, 2345 would be a legitimate entry.

5.     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.

You are trying to estimate the average amount a family spends on food during a year. In the past, the standard deviation of the amount a family has spent on food during a year has been \$1200. If you want to be 99% sure that you have estimated average family food expenditures within \$60, how many families do you need to survey? Place your answer, a whole number, in the blank . For example, 1234 would be a legitimate entry.

6.     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.

Senior management of a consulting services firm is concerned about a growing decline in the firm’s weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the management randomly selected a sample of size 51 from the available frame. The sample mean and sample standard deviations were 48.5 and 7.5 hours, respectively.

Construct a 95% confidence interval for the standard deviation of the number of hours this firm’s employees spend on work-related activities in a typical week.

Place your LOWER limit, in hours, rounded to 1 decimal place, in the first blank. For example, 6.7 would be a legitimate entry.

Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3 would be a legitimate entry.

 7.     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.

8.     In constructing a confidence interval estimate for a population mean, when we replace with the sample standard deviation (s), we introduce a new source of variability and the sampling distribution we use is:

 A.F- distribution B.the normal distribution C.t -distribution D.chi-square distribution

9.     The t- distribution for developing a confidence interval for a mean has _____ degrees of freedom.

 A.n – 1 B.n C.n – 2 D.n + 1

10.  From a sample of 500 items, 30 were found to be defective. The point estimate of the population proportion defective will be:

 A..06 B.30 C.0.60 D.16.667

11.  The average gas mileage of a certain model car is 26 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.3, find the probability that a randomly selected car of this model has a gas mileage between 25.8 and 26.3 miles per gallon.

 A.0.15 B.0.85 C.0.70 D.0.30

12.  When you calculate the sample size for a proportion, you use an estimate for the population proportion; namely . A conservative value for n can be obtained by using = ______ .

 A.0.05 B.0.01 C.0.50 D.0.10

13.  A sample of 23 European countries found that the variance of life expectancy was 7.3 years. What is the 95% confidence interval estimate for the variance of life expectancy in Europe?

14.  A previous study of nickels showed that the standard deviation of the weight of nickels is 150 milligrams. How many nickels does a coin counter manufacturer need to weigh so that she can be 98% confident that her sample mean is within 25 milligrams of the true average weight of a nickel?

 A.36 B.196 C.239 D.139

15.  At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years. If the number of years of employment at this department store is normally distributed, what is the probability that a cashier selected at random has worked at the store for over 10 years?

 A.0.4916 B.0.9916 C.0.0084 D.0.0054

16.  Compute where t15 has a t-distribution with 15 degrees of freedom.

 A.0.03197 B.0.96803 C.0.7639 D.0.93606

In

I17. In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that SAT test scores are normally distributed with a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?

 A.1330 B.1400 C.1250 D.1100

18.A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval estimate for the true proportion of women in Europe who use the Internet?

 A.0.321 < p < 0.379 B.0.316 < p < 0.384 C.0.309 < p < 0.391 D.0.305 < p < 0.395

19.As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion, , only if the sample size n is greater than 30.

 True False

20.The lower limit of the 95% confidence interval for the population proportion p, given that n = 300; and = 0.10 is 0.1339.

 True False

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