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Statistics homework 5, Assignments of Business Statistics

University of California - DavisBusiness Statistics

This is the homework of my statistics course STA013, hope it’ll help any of you guys.

Typology: Assignments

2022/2023

Uploaded on 12/14/2023

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Homework 5
T/F (Mark T if the statement is true or F if the statement is false.)
1. An interval estimate is an interval that provides an upper and lower bound for a specific
population parameter whose value is unknown.
2. A point estimate is a single number that is used as an estimate of a population parameter
or population characteristic. It is usually derived from a random sample from the
population of interest.
3. An unbiased estimator of a population parameter is an estimator whose variance is the
same as the actual value of the population variance.
4. An estimator is unbiased if the mean of its sampling distribution is equal to the true value
of the population parameter being estimated.
5. If a store manager is interested in estimating the mean amount spent per customer per
visit at her store, the sample mean would be the appropriate point estimate.
6. If Joe Biden's campaign manager is interested in estimating the proportion of registered
voters who will support Biden on November 5nd, 2024, the sample proportion would be
the appropriate point estimate.
7. As the sample size increases and other factors are the same, the width of a confidence
interval for a population mean tends to decrease.
8. Suppose a 95% confidence interval for the mean height of a 12-year-old male in the
United States is 54 to 65 inches. It can be said that 95% of 12-year-old males in the U.S.
have height greater than or equal to 54 inches and less than or equal to 65 inches.
9. If the population variance is increased and other factors are the same, the width of a
confidence interval for the population mean tends to increase.
10. The confidence coefficient is the probability that a confidence interval will enclose the
estimated parameter.
11. A 90% confidence interval estimate for a population mean is determined to be 62.8 to
73.4. If the confidence level is reduced to 80%, the confidence interval for becomes
narrower.
12. When constructing a confidence interval for a population parameter, we generally set the
confidence coefficient ( ) close to 0 (usually between 0 and 0.05) because it is the
probability that the interval does not include the actual value of the population parameter.
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Homework 5 T/F (Mark T if the statement is true or F if the statement is false.)

  1. An interval estimate is an interval that provides an upper and lower bound for a specific population parameter whose value is unknown.
  2. A point estimate is a single number that is used as an estimate of a population parameter or population characteristic. It is usually derived from a random sample from the population of interest.
  3. An unbiased estimator of a population parameter is an estimator whose variance is the same as the actual value of the population variance.
  4. An estimator is unbiased if the mean of its sampling distribution is equal to the true value of the population parameter being estimated.
  5. If a store manager is interested in estimating the mean amount spent per customer per visit at her store, the sample mean would be the appropriate point estimate.
  6. If Joe Biden's campaign manager is interested in estimating the proportion of registered voters who will support Biden on November 5nd, 2024, the sample proportion would be the appropriate point estimate.
  7. As the sample size increases and other factors are the same, the width of a confidence interval for a population mean tends to decrease.
  8. Suppose a 95% confidence interval for the mean height of a 12 - year-old male in the United States is 54 to 65 inches. It can be said that 95% of 12 - year-old males in the U.S. have height greater than or equal to 54 inches and less than or equal to 65 inches.
  9. If the population variance is increased and other factors are the same, the width of a confidence interval for the population mean tends to increase.
  10. The confidence coefficient is the probability that a confidence interval will enclose the estimated parameter.
  11. A 90% confidence interval estimate for a population mean is determined to be 62.8 to 73.4. If the confidence level is reduced to 80%, the confidence interval for becomes narrower.
  12. When constructing a confidence interval for a population parameter, we generally set the confidence coefficient ( ) close to 0 (usually between 0 and 0.05) because it is the probability that the interval does not include the actual value of the population parameter. ⼀ T F ⼚ T ⼀ T F T F ⼀ F
  1. The wider the confidence interval, the more likely it is that the interval contains the true value of the population parameter.
  2. A 95% confidence interval for the population proportion p is found to be between. and .336. Based on this information, the sample proportion that generated the confidence interval was .122.
  3. One way to reduce the margin of error in a confidence interval is to decrease the confidence coefficient.
  4. Suppose a 90% confidence interval for the mean time it takes to serve a customer at a drive-in bank is 120 seconds to 220 seconds. At the 90% confidence level, there is not enough evidence to conclude that the mean service time is not 200 seconds.
  5. In estimating the difference between two population means, if a 90% confidence interval estimate includes zero, then we can conclude that there is a 90% chance that the difference between the two population means is zero. Multiple Choices (Choose the option that best answers question)
  6. An unbiased estimator is: a. any sample statistic used to approximate a population parameter b. (^) a sample statistic, which has an expected value equal to the value of the population parameter c. (^) a sample statistic whose value is usually less than the value of the population parameter d. a sample statistic whose value is usually greater than the value of the population parameter e. (^) any estimator whose standard error is relatively small
  7. From a sample of 200 items, 12 items are defective. The point estimate of the population proportion defective will be: a. (^12) b. (^) 0. c. (^) 16. d. (^) 0. e. (^) 1.
  8. The type of sample statistic that is used to make inferences about a given type of population parameter is called: a. the estimator of that parameter b. (^) the confidence level of that parameter c. (^) the confidence interval of that parameter ⼀ F not the (^) specific sample proportion F (^) - increasing sample^ size^ or^ reduciongvariability^ can^ reduce^ the (^) margin of error, T

F

b b 品 : 0.^06 a

e. (^) 69.00 1.

  1. The use of the standard normal distribution for constructing confidence interval estimate for the population proportion p requires: a. (^) and are both greater than 5, where is the sample proportion b. (^) np and n (1 – p ) are both greater than 5 c. (^) ( p + ) and ( p – ) are both greater than 1 d. (^) that the sample size is greater than 5 e. (^) np and n (1 – p ) are both greater than 1
  2. The lower limit of a confidence interval at the 95% level of confidence for the population proportion if a sample of size 100 had 30 successes is: a. (^) 0. b. (^) 0. c. 0. d. (^) 0. e. (^) 0.
  3. A random sample of 400 Michigan State University (MSU) students were surveyed recently to determine an estimate for the proportion of all MSU students who had attended at least three football games. The estimate revealed that between .372 and .458 of all MSU students attended. Given this information, we can determine that the confidence coefficient was approximately: a. (^). b.. c. (^). d. (^). e. (^).
  4. A 95% confidence interval for the population proportion of professional tennis players who earn more than 2 million dollars a year is found to be between .82 and .88. Given this information, the sample size that was used was approximately: a. (^545) b. 382 c. (^233) d. (^387) e. (^480)
  5. In constructing a 95% confidence interval estimate for the difference between the means of two normally distributed populations, where the unknown population variances are assumed not

, b

b,

台 = 器 =^0.^3

2 =^1. 9 = (^0). 2102 , (^0.^3898 ) “ a 1 -^ α=^0. 995

p :

(^0) , 82 + (^0). (^88) =^0. 85 入^1 -^95 % n = (

s) ×

⼀- (^) = (^0). 05 0. 85 × 0. <^5 α

1 - 台 =^0.^15 Ʃ= 0.^25

E =^ (^0.^88

  • (^0). 85 ) = (^0). 03 (^2) ≡= 20. 025 =^1.^96 = 544. 2266 b

to be equal, summary statistics computed from two independent samples are: , , , , , and. The upper confidence limit is: a. (^) 18. b. (^) 6. c. (^) 5. d. 77. e. (^) 89.

  1. The z - value needed to construct a 97.8% confidence interval estimate for the difference between two population proportions is: a. (^) 2. b. (^) 2. c. (^) 2. d. (^) 1. e. 1.

  2. If you wish to construct 98% upper confidence bound (UCB) for the difference between population proportions, then the approximate z - value you should use is: a. (^) 2. b. (^) 2. c. (^) 1. d. (^) 1. e. (^) 1.

  3. Suppose you wish to estimate a population proportion p based on sample of n observations. How large should a sample be if you want your estimate to be within .03 of p with probability equal to 0.90? a. (^752) b. (^423) c. (^) 1, d. 1. e. none of these

  4. Suppose you wish to estimate a population mean based on a sample of n observations. How large should a sample be if you want your estimate to be within 2 of with probability equal to 0.95 if you know the population standard deviation is 12? a. 239 b. (^196)