# Suppose A Random Sample Of 36 Is Selected From A Population With A Standard Deviation Of 12.

Question 1

Suppose a random sample of 36 is selected from a population with a standard deviation of 12. If the sample mean is 98, the 90% confidence interval for the population mean is __________ .

[removed] | 94.71 to 101.29 | |

[removed] | 97.45 to 98.55 | |

[removed] | 94.08 to 101.92 | |

[removed] | 97.35 to 98.65 | |

[removed] | 95.00 to 105.00 |

Question 2

Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 95% confidence interval for the population mean of waiting times is _________ .

[removed] | 14.02 to 15.98 | |

[removed] | 7.16 to 22.84 | |

[removed] | 14.06 to 15.94 | |

[removed] | 8.42 to 21.58 | |

[removed] | 19.80 to 23.65 |

Question 3

James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. His staff randomly selected personnel files for 100 tellers in the Southeast Region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 95% confidence interval for the population mean of training times is _________ .

[removed] | 15.20 to 34.80 | |

[removed] | 24.18 to 25.82 | |

[removed] | 24.02 to 25.98 | |

[removed] | 16.78 to 33.23 | |

[removed] | 23.32 to 35.46 |

Question 4

A researcher is interested in estimating the mean value for a population. She takes a random sample of 17 items and computes a sample mean of 224 and a sample standard deviation of 32. She decides to construct a 98% confidence interval to estimate the mean. The degrees of freedom associated with this problem are _________ .

[removed] | 18 | |

[removed] | 17 | |

[removed] | 16 | |

[removed] | 15 | |

[removed] | 20 |

Question 5

The lengths of steel rods produced by a shearing process are normally distributed. A random sample of 10 rods is selected; the sample mean length is 119.05 inches; and the sample standard deviation is 0.10 inch. The 95% confidence interval for the population mean rod length is ___________ .

[removed] | 118.99 to 119.11 | |

[removed] | 118.82 to 119.28 | |

[removed] | 118.98 to 119.12 | |

[removed] | 118.85 to 119.25 | |

[removed] | 119.89 to 122.12 |

Question 6

A random sample of 225 items from a population results in 60% possessing a given characteristic. Using this information, the researcher constructs a 99% confidence interval to estimate the population proportion. The resulting confidence interval is _________ .

[removed] | 0.54 to 0.66 | |

[removed] | 0.59 to 0.61 | |

[removed] | 0.57 to 0.63 | |

[removed] | 0.52 to 0.68 | |

[removed] | 0.68 to 0.76 |

Question 7

A study is going to be conducted in which a population mean will be estimated using a 92% confidence interval. The estimate needs to be within 12 of the actual population mean. The population variance is estimated to be around 2500. The necessary sample size should be at least __________ .

[removed] | 15 | |

[removed] | 47 | |

[removed] | 53 | |

[removed] | 638 | |

[removed] | 700 |

Question 8

A study will be conducted to estimate the population proportion. A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least __________ .

[removed] | 1036 | |

[removed] | 160 | |

[removed] | 41 | |

[removed] | 259 | |

[removed] | 289 |

Question 9

In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 0.10, the rejection region would be _________ .

[removed] | z > 1.64 | |

[removed] | z > 1.28 | |

[removed] | z < -1.28 and z > 1.28 | |

[removed] | z < -1.64 and z > 1.64 | |

[removed] | z < -2.33 and z > 2.33 |

Question 10

A company produces an item that is supposed to have a six inch hole punched in the center. A quality control inspector is concerned that the machine which punches the hole is “out-of-control” (hole is too large or too small). In an effort to test this, the inspector is going to gather a sample punched by the machine and measure the diameter of the hole. The alternative hypothesis used to statistical test to determine if the machine is out-of-control is

[removed] | the mean diameter is > 6 inches | |

[removed] | the mean diameter is < 6 inches | |

[removed] | the mean diameter is = 6 inches | |

[removed] | the mean diameter is ≠ 6 inches | |

[removed] | the mean diameter is ≥ 6 inches |

Question 11

Ophelia O’Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is “no more than 5% of personal loans should be in default.” On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday’s sample contained 30 defaulted loans. Ophelia’s null hypothesis is ________ .

[removed] | p > 0.05 | |

[removed] | p = 0.05 | |

[removed] | n = 30 | |

[removed] | n = 500 | |

[removed] | n = 0.05 |

Question 12

Ophelia O’Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is “no more than 5% of personal loans should be in default.” On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday’s sample contained 30 defaulted loans. Using α = 0.10, the critical z value is _________ .

[removed] | 1.645 | |

[removed] | -1.645 | |

[removed] | 1.28 | |

[removed] | -1.28 | |

[removed] | 2.28 |

Question 13

Ophelia O’Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is “no more than 5% of personal loans should be in default.” On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday’s sample contained 30 defaulted loans. Using α = 0.10, the observed z value is ________ .

[removed] | 1.03 | |

[removed] | -1.03 | |

[removed] | 0.046 | |

[removed] | -0.046 | |

[removed] | 1.33 |

Question 14

Ophelia O’Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is “no more than 5% of personal loans should be in default.” On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday’s sample contained 30 defaulted loans. Using α = 0.10, the appropriate decision is ________ .

[removed] | reduce the sample size | |

[removed] | increase the sample size | |

[removed] | reject the null hypothesis | |

[removed] | do not reject the null hypothesis | |

[removed] | do nothing |

Question 15

Ophelia O’Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is “no more than 5% of personal loans should be in default.” On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday’s sample contained 38 defaulted loans. Using α = 0.10, the appropriate decision is ________ .

[removed] | reduce the sample size | |

[removed] | increase the sample size | |

[removed] | reject the null hypothesis | |

[removed] | do not reject the null hypothesis | |

[removed] | do nothing |

Question 16

The manufacturer of an over-the-counter heartburn relief mediation claims that its product brings relief in less than 3.5 minutes, on average. To be able to make this claim the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the standard deviation was 1.1 minutes. Calculate the appropriate test statistic to test the hypotheses.

[removed] | 1.29 | |

[removed] | 9.09 | |

[removed] | -1.29 | |

[removed] | -2.58 | |

[removed] | -9.09 |

Question 17

A company has developed a new ink-jet cartridge for its printer that it believes has a longer life-time on average than the one currently being produced. To investigate its length of life, 225 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages, respectively. The historical average lifetime for cartridges produced by the current process is 1502.5 pages. Calculate the appropriate test statistic to test the hypotheses.

[removed] | 56.09 | |

[removed] | 3.74 | |

[removed] | 22.34 | |

[removed] | -3.74 | |

[removed] | -22.34 |

Question 18

In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 miles and a standard deviation of 37,500 miles. Calculate the appropriate test statistic to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

[removed] | 2.47 | |

[removed] | 34.13 | |

[removed] | 478.16 | |

[removed] | -34.13 | |

[removed] | -2.47 |

Question 19

Standard x-ray machines should give radiation dosages below 5.00 mill roentgens. To test a certain x-ray machine a sample of 36 observations is taken with a mean of 4.13 m. and a standard deviation of 1.91 m. Calculate the appropriate test statistic to test the hypotheses.

[removed] | -2.73 | |

[removed] | -3.78 | |

[removed] | -0.455 | |

[removed] | 3.78 | |

[removed] | 2.73 |

Question 20

A researcher is studying the number of times a person uses their ATM/Debit card to make a purchase in a 30-day period. The researcher believes that the average number of ATM/Debit card transactions is 32 per month. A sample of 30 individuals is taken, and it is determined that for the sample the mean is 36, with a sample standard deviation of 1.6. Based on the sample, is their sufficient evidence to conclude that the average number of ATM/Debit card transactions per month is actually greater than 32? Test the Hypothesis at a 0.05 level of significance.

The Null Hypothesis is: Ho: μ Blank 1[removed]

The Alternative Hypothesis is: Ha: μ Blank 2[removed]

The Critical Value at a 0.05 Level of Significance is: Blank 3[removed]

The Calculated Test Statistic is: Blank 4[removed]

The decision based on the Critical Value and the p-value approach is to: Blank 5[removed]

Question 21

The National Christmas Decor Foundation believes that 70% of all homes in the US decorate using white lights. The Christmas Shoppe collected data from 100 homes in their market to determine if the homeowners intended to decorate the exterior of their homes with white lights. Of the 100 homes surveyed, 63 indicated that they would indeed use white lights. At a 0.01 level of significance, is their sufficient evidence to conclude that the proportion of homes using white lights as Christmas decoration is actually lower than the 70% claimed by the NCDF?

The Null Hypothesis is p [removed] 0.70

The Alternative Hypothesis is p [removed] 0.70

The Critical Value for this test is [removed]

The calculated Test Statistic for this test is [removed]

The decision, based on the above information is to [removed] the Null Hypothesis.

Question 22

Determine the p-value for H0: p = .5 versus Ha: p ≠.5 when n = 225 and = .54. (Carry your answer to 4 decimal places).

[removed]

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