ST 260 Exam 2
Assume a Standard Normal Distribution: If P(X <= Z) = .3745, Z=
-0.32
Assume a Standard Normal Distribution: P(X >= 1.20)
.1151
Assume a Standard Normal Distribution: P(0 <= X <= 1.20)
.3849
Assume a Standard Normal Distribution: P(-1.5 <= X <= .72)
.6974
Assume a Standard Normal Distribution: P(X <= 1.20)
.8849
Assume a Standard Normal Distribution: P(-1.2 <= Z <= .58) a) .6039 b) .7190 c) .7022 d) .6358 e) .1151
A
Assume a Standard Normal Distribution: P(Z >= 1.06) a) .1446 b) .9452 c) .0548 d) .8554 e) .2577
A
A fast-food corporation wants to study drive-thru times at their restaurants. From their historical data, it is known that the time to serve a customer is normally distributed with a mean of 60 seconds and a standard deviation of 10 seconds. A-> What is the probability that a future customer will complete their drive-thru service in 40 seconds or less? B-> More than 52 seconds? C-> Between 44 and 62 seconds? D-> At what amount of seconds will 69.15% (P=.6915) of all drive-thru customers complete their service in that time or less?
A) .6228 B) C) .5245 D) 65 seconds
Sumo wrestlers weight is known to have a Normal Distribution. From a sample of 36 Sumo Wrestlers the average weight was found to be 300 lbs. It is known that the population standard deviation (σ) of Sumo wrestlers is 18 lbs. A-> Calculate a 90% Confidence Interval around the mean B-> It has been hypothesized that the true mean weight of Sumo wrestlers is 310 lbs. Do you find this to be a plausible value given the result of your confidence interval?
A) 300 ± 2.4867 B)
The USDA is interested in knowing if the Tastes Good Peanut Company is really keeping to their claim of actually providing 50 lbs of Peanuts in their "50 Pound Bag" that they sell to the general public. To test this, the auditor takes a sample of 100 bags of peanuts and calculates their mean weight. He finds from his sample of 100 bags that the Sample Mean weight is 49.8 lbs and that the Sample Standard Deviation is 1.5 lbs. A-> Calculate a 90% Confidence Interval around the mean B-> As the auditor, do you find this to be a plausible value to support that the company is putting at least 50 lbs of peanuts in their "50 Pound Bag" given the result of your confidence interval? C-> If you were to use a 80% Confidence Level instead, would that change your decision? Why/Why not?
A) 49.8 ± .249 B) C)
Suppose ACT scores are known to be normally distributed with a mean (μ) of 24 and a population standard deviation (σ) of 4: What is the probability that someone that takes the ACT will achieve a score of 20 or less? (4 points) a) .6915 b) .1587 c) .3085 d) .0668 e) .8413
B
The FDA is interested in knowing if the "Tater Jim's" 10-pound sack of potatoes is really keeping to their claim of actually providing 10 lbs. of potatoes in their "10 Pound Bag" that they sell to the general public. To test this, the auditor takes a sample of 49 bags of peanuts and calculates their mean weight. He finds that the Sample Mean weight is 9.8 lbs. and that the Sample Standard Deviation (s) is .70 lbs. -> Calculate a 95% Confidence Interval around the mean. a. (9.5990, 10.0010) b. (9.5989, 10.0011) c. (9.6323, 9.9677) d. (9.6040, 9.9960) e. (9.6355, 9.9645) -> As the auditor, do you find this to be a plausible value to support that the company is putting at least 10 lbs of potatoes in their "10 Pound Bag" given the result of your confidence interval? . (3 points) a. Yes, because the hypothesized value of 10 lbs. falls in my 95% confidence interval. b. Yes, because the hypothesized value of 10 lbs is less than a Z-value of 2.5 c. Yes, because the hypothesized value of 10 lbs is within 1 standard deviation of the sample mean. d. No, because the hypothesized value of 10 lbs is NOT within 1 standard deviation of the sample mean. e. No, because the hypothesized value of 10 lbs does not fall in my 95% confidence interval. -> If you were to use a 90% Confidence Level instead, would that change your decision? Why or why not? (4 points) a. No, because the hypothesized value of 10 lbs. falls in my 90% confidence interval. b. No, because the hypothesized value of 10 lbs is less than a Z-value of 2.5 c. No, because the hypothesized value of 10 lbs is within 1 standard deviation of the sample mean. d. Yes, because the hypothesized value of 10 lbs is NOT within 1 standard deviation of the sample mean. e. Yes, because the hypothesized value of 10 lbs does not fall in my 90% confidence interval.
B, A, E
A Type 1 error occurs when: a- one accepts the Null Hypothesis and it is actually false b- one uses the incorrect test statistic when calculating a confidence interval c- one rejects the null hypothesis and it is actually true d- one rejects the null hypothesis based on an incorrect calculation e- one assumes that the sampling distribution is normal when it is not
C
A Type I error occurs when: a. One accepts the Null Hypothesis and it is actually false b. One uses the incorrect test statistic when calculating a confidence interval c. One rejects the Null Hypothesis and it is actually true d. One rejects the Null Hypothesis based on an incorrect calculation e. One assumes that the sampling distribution is normal when it is not
C
Assume a Standard Normal Distribution: If P(-Z <= X <= Z) = .7580, ±Z= a) ± 1.25 b) ± 0.70 c) ± 1.17 d) ± 0.85 e) ± 1.02
C
Assume a Standard Normal Distribution: P(0 <= Z <= 1.06) a) .1446 b) .5000 c) .3554 d) .8554 e) .5544
C
For any Normal Distribution: Approximately _________ of the data falls between ± 1 Standard Deviation of the mean. a. 50% b. 62% c. 68% d. 95% e. 99.7%
C
Suppose ACT scores are known to be normally distributed with a mean (μ) of 24 and a population standard deviation (σ) of 4: With a score of 26 or more? (4 points) a) .6915 b) .1587 c) .3085 d) .0668 e) .8413
C
What is the appropriate t-statistic for a 90% Confidence Interval from a sample of size 14? a) 1.645 b) 1.761 c) 1.771 d) 2.160 e) 2.145
C
Assume a Standard Normal Distribution: P(X <= Z) = .2005, Z= a) 1.84 b) -1.2 c) -.81 d) -.84 e) .84
D
Assume a Standard Normal Distribution: P(Z <= 1.06) a) .1446 b) .9452 c) .0548 d) .8554 e) .8577
D
For any Normal Distribution: Approximately _________ of the data falls between ± 2 Standard Deviation of the mean. a. 50% b. 62% c. 68% d. 95% e. 99.7%
D
Suppose ACT scores are known to be normally distributed with a mean (μ) of 24 and a population standard deviation (σ) of 4: At what score will the top 01.22% (P=.0122) of all ACT test takers make that score or more? (4 points) a) 15 b) 16 c) 32 d) 33 e) 34
D
Which of the following is NOT included when writing a conclusion in the language of the problem (LOP)? a- the level of confidence b- the parameter being estimated c- the population to which we generalize to d- the standard error e- the confidence interval
D
Which of the following is NOT included when writing a conclusion in the language of the problem (LOP)? a) The Level of Confidence b) The Parameter being estimated c) The Population to which we generalize to d) The Standard Error e) The Confidence Interval
D
Which of the following is NOT true about the t-distribution? a- it is slightly larger (fatter) than the standard normal (z) distribution b- it was discovered by a brewmaster at the Guiness brewery in Ireland c- the penalty for using (s) instead of (σ) is reflected in the degrees of freedom d- it results in smaller intervals than when calculating confidence intervals with the same level of confidence as those using the standard normal (z) distribution e- as the sample size gets larger, the t-distribution approaches (gets closer to) the corresponding standard normal (z) distribution value
D
Which of the following is NOT true about the t-distribution? a. It is slightly larger (fatter) than the Standard Normal (Z) distribution b. It was discovered by a brewmaster at the Guiness brewery in Ireland c. The penalty for using (s) instead of (σ) is reflected in the degrees of freedom d. It results in smaller intervals than when calculating confidence intervals with the same level of confidence as those using the standard normal (Z) distribution. e. As the sample size gets larger, the t-distribution approaches (gets closer to) the corresponding standard normal (Z) distribution value.
D
The one-year postgraduate salary of statistics students is known to have a Normal Distribution. From a sample of 64 statistics students, the average salary was found to be $60,000. It is known that the population standard deviation (σ) of salaries of statisticians one-year post graduation is $8.000. -> Calculate a 95% Confidence Interval around the mean. a. ($58,718, $61,282) b. ($58,355, $61,645) c. ($57,674, $62,326) d. ($58,040, $61,960) e. ($57,424, $62,576) -> It has been hypothesized that the true mean one-year postgraduate salary of statistics students is $58,400. Do you find this to be a plausible value given the result of your confidence interval? a. Yes, because the hypothesized value of $58,400 falls in my 95% confidence interval. b. Yes, because the hypothesized value of $58,400 is less than a Z-value of 2.5 c. Yes, because the hypothesized value of $58,500 is within 1 standard deviation of the sample mean. d. No, because the hypothesized value of $58,500 is NOT within 1 standard deviation of the sample mean. e. No, because the hypothesized value of $58,400 does not fall in my 95% confidence interval.
D, A
Assume a Standard Normal Distribution: P(Z <= 0) a) .3038 b) .0228 c) .0668 d) .6915 e) .5000
E
For any Normal Distribution: Approximately ____________ of the data falls between ± 3 Standard Deviation of the mean. a. 50% b. 62% c. 68% d. 95% e. 99.7%
E
Suppose ACT scores are known to be normally distributed with a mean (μ) of 24 and a population standard deviation (σ) of 4: With a score between 20 and 26? (4 points) a) .3830 b) .6915 c) .5427 d) .7122 e) .5328
E
T/F: As the level of confidence gets smaller, the width of a confidence interval gets larger.
False
T/F: Degrees of Freedom are associated with the Z statistic
False
T/F: If one *does not know* the Population Standard Deviation and must estimate it with the Sample Standard Deviation, then one should use a Z statistic instead of a t statistic when calculating confidence intervals.
False
T/F: If the confidence level is .88 (88%), then the level of risk (α) = .06
False
T/F: If the underlying distribution of the variable of interest is NOT normal, than we can assume that the distribution of sample means is also normal, regardless of the sample size.
False
T/F: (?) is at the dead center of a confidence interval calculated from a sample
True
T/F: A Standard Normal Distribution is one that has a mean of 0 and a standard deviation of 1.
True
T/F: After an event occurs, the probability that that event was a success is either 0 (no success) or 1 (success)
True
T/F: Any normal distribution can be transformed into a standard normal distribution.
True
T/F: As the level of confidence gets larger, the width of a confidence interval gets larger.
True
T/F: If one *does not know* the Population Standard Deviation and must estimate it with the Sample Standard Deviation, then one should use a t statistic instead of a Z statistic when calculating confidence intervals.
True
T/F: If the underlying distribution of the variable of interest is already normal, than we can assume that the distribution of sample means is also normal, regardless of the sample size
True
T/F: The Central Limit Theorem states that the sampling distribution of the mean is approximately normal no matter what the underlying distribution is as long as the sample size is large enough (n >= 30)
True
T/F: The standard deviation (i.e. "Standard Error") of a sampling distribution where the population standard deviation is known is (?)
True
T/F: The standard deviation of a sampling distribution is σ / [sq. root of n]
True
T/F: Two things that characterize a Normal Distribution are a bell-shaped curve and symmetry around the mean
True