Deck 5: Statistical Inference

Question 1

< p >If the average derived from a specific sample is $43,000, then = 43,000 is the __________ of the population mean.< / p>

A) deviation
B) estimate
C) point
D) static point

Answer 1

estimate

Question 2

In a population set, 14 students of the 137 observations received a failing grade in the Accounting Principles course. What is the estimate of the sample proportion of failure in the course?

A) 0.1022
B) 9.786
C) 0.6879
D) 0.0102

Answer 2

0.1022

Question 3

In a population set, 13 students of the 132 observations received a failing grade in the Accounting Principles course. What is the estimate of the sample proportion of failure in the course?

A) 0.0985
B) 10.154
C) 0.6842
D) 0.0099

Answer 3

0.0985

Question 4

Cameron is the quality inspector for the Mason Pot Company, an artesian cooperative crafting bowls. In the smaller series, the mean diameter is 3 inches with a standard deviation of 0.3 inch. First, find the expected value. Then answer: what is the standard error of the sample mean derived from a random sample of 24 bowls?

A) 0.061
B) 0.6
C) 0.002
D) 0.24

Question 5

Cameron is the quality inspector for the Mason Pot Company, an artesian cooperative crafting bowls. In the smaller series, the mean diameter is 4 inches with a standard deviation of 0.2 inch. First, find the expected value. Then answer: what is the standard error of the sample mean derived from a random sample of 12 bowls?

A) 0.058
B) 0.58
C) 0.001
D) 0.12

Question 6

Megan ran an analysis with a population standard deviation? = 0.90. When reviewing sample sizes of 4 and 8, the standard error for the sample mean was = 0.45 and = 0.32 respectively. Doing a comparison, what does the expected value and the standard error of the sample mean reflect?< / p>

A) By comparison, the results confirm the sample is normally distributed with increased variability.
B) The standard error for the sample mean is lower confirming the initial population standard deviation is incorrect.
C) By comparing, the results confirm that averaging reduces variability.
D) The standard error for the sample mean is lower, increasing variability in the sample set.

Question 7

The Central Limit Theorem, by definition, implies that as the sample size increases, the

A) average of the large number of independent observations has an approximate normal distribution.
B) average of the large number of independent observations reflects the leftmost tail of the distribution.
C) expected underlining distribution is only justified when n $\le$ 30.
D) expected normal distribution declines.

Question 8

What is the expected value of the sample proportion?

A) number of success
B) sample population
C) standard error
D) population proportion

Question 9

CNBC (2018) reported 53% of households are using streaming services compared to standard cable. What are the expected value and the standard error of the sample proportion derived from a random sample of 600?

A) EP¯ = 0.47 and seP¯ = 0.0204
B) EP¯= 0.0204 and seP¯ = 0.47
C) EP¯= 0.53 and seP¯ = 0.0204
D) EP¯= 0.7115 and seP¯ = 0.0324

Question 10

CNBC (2018) reported 58% of households are using streaming services compared to standard cable. What are the expected value and the standard error of the sample proportion derived from a random sample of 500?

A) = 0.42 and <em> </em> = 0.0221< / p>
B) = 0.0221 and <em> </em> = 0.42< / p>
C) = 0.58 and <em> </em> = 0.0221< / p>
D) = 0.7615 and <em> </em> = 0.0341< / p>

Question 11

A range of values used to estimate a population parameter of interest is called

A) estimated error.
B) confidence interval.
C) standard error.
D) probability of success.

Question 12

In a meeting, Matt estimates the average miles per gallon (mpg) of the fleet cars is 19 mpg. With a certain level of confidence, he announces the actual mpg is in the 16 to 22 mpg range. What is the Margin of Error?

A) 6 mpg
B) 0.50 mpg
C) 19 mpg
D) 3 mpg

Question 13

In a meeting, Matt estimates the average miles per gallon (mpg) of the fleet cars is 24 mpg. With a certain level of confidence, he announces the actual mpg is in the 22 to 26 mpg range. What is the Margin of Error?

A) 4 mpg
B) 0.50 mpg
C) 24 mpg
D) 2 mpg

Question 14

If the confidence coefficient is 0.77, what is the implied probability of error $\alpha$ ?

A) 0.23
B) 0.77
C) 1
D) 0.5

Question 15

If the confidence coefficient is 0.85, what is the implied probability of error $\alpha$ ?

A) 0.15
B) 0.85
C) 1
D) 0.05

Question 16

IIn a sample of 37, the mean is confidence interval for the population mean. The t Table = 1.688.

A) 90% confidence interval is 93.38± 2.84.
B) 90% confidence interval is 95.92.
C) 90% confidence interval is between 90.84 and 95.92.
D) 90% confidence interval is 93.28± 1.688.

Question 17

<p>In a sample of 25, the mean is = 86.92 with a standard deviation of s = 9.87. Assuming the results follow a normal distribution, construct the 90% confidence interval for the population mean. The t Table = 1.711.

A) 90% confidence interval is 86.92± 3.68.
B) 90% confidence interval is 90.30.
C) 90% confidence interval is between 83.54 and 90.30.
D) 90% confidence interval is 86.82± 1.711.

Question 18

In a sample of 23, the mean is confidence interval for the population mean. The t Table = 1.717.

A) 90% confidence interval is 90.88± 95.90.
B) 90% confidence interval is 2.51.
C) 90% confidence interval is between 90.71 and 96.07.
D) 90% confidence interval is 90.88± 1.72.

Question 19

<p>In a sample of 60, the mean is = 76.29 with a standard deviation of s = 7. Assuming the results follow a normal distribution, construct the 90% confidence interval for the population mean. The t Table = 1.684.

A) 90% confidence interval is 76.29± 1.52
B) 90% confidence interval is 77.97.
C) 90% confidence interval is between 74.61 and 77.97.
D) 90% confidence interval is 76.29± 1.684.

Question 20

In a sample of 19, and x¯= 81, with a standard deviation of s = 7, the standard error of the sample mean is

A) 0.684
B) 1.606
C) 1.725
D) 2.717

Question 21

<p>In a sample of 9, and<em> = 76, with a standard deviation of s = 5, the standard error of the sample mean is

A) 0.745
B) 1.667
C) 1.786
D) 2.778

Question 22

In a sample of 33, 9 were found to have over 200 Blu-Ray Discs in one location. Construct the point estimate for the population proportion.

A) 0.54
B) 0.01
C) 0.14
D) 0.27

Question 23

In a sample of 30, 9 were found to have over 200 Blu-Ray Discs in one location. Construct the point estimate for the population proportion.

A) 0.60
B) 0.045
C) 0.15
D) 0.30

Question 24

In a sample of 23 iPhones, 10 had over 83 apps downloaded. Construct a 90% confidence interval for the population proportion of all iPhones that obtain over 83 apps. Assume z_0.05 = 1.645.

A) 0.43± 0.17
B) 0.43± 0.08
C) 0.27± 0.16
D) 0.27± 0.17

Question 25

In a sample of 25 iPhones, 12 had over 85 apps downloaded. Construct a 90% confidence interval for the population proportion of all iPhones that obtain over 85 apps. Assume z_0.05 = 1.645.

A) 0.48± 0.16
B) 0.48± 0.09
C) 0.29± 0.15
D) 0.29± 0.16

Question 26

In a sample of 62 iPhones, 18 had over 100 apps downloaded. Construct a 99% confidence interval for the population proportion of all iPhones that obtain over 100 apps. Assume z_0.005 = 2.576.

A) 0.18± 0.15
B) 0.18± 0.09
C) 0.29± 0.14
D) 0.29± 0.15

Question 27

In a sample of 50 iPhones, 13 had over 100 apps downloaded. Construct a 99% confidence interval for the population proportion of all iPhones that obtain over 100 apps. Assume z_0.005 = 2.576.

A) 0.13± 0.16
B) 0.13± 0.09
C) 0.26± 0.15
D) 0.26± 0.16

Question 28

According to the National Retail Federation, the average shopper will spend $1,007.24 during the holiday shopping season. What is the null and alternate hypothesis?

A) Sample Population is needed to complete the hypothesis.
B) H₀: $\mu$ $\neq$ 1007.24; H_A $\mu$ = 1007.24
C) H₀: $\mu$ $\ge$ 1007.24; H_A $\mu$ $\le$ 1007.24
D) H₀: $\mu$ = 1007.24; H_A $\mu$ $\neq$ 1007.24

Question 29

Peter provided an analysis for the building of a multi-unit retail strip for Corning Construction using the following hypothesis:H₀: $\mu$ = Do not build the Strip Mall; Build the Strip Mall. Based on his calculations of the area, and the probabilities for growth, he shows the project will be profitable. The client built the strip mall to a profit loss. What type of error would this represent?

A) Type I error because the building was built.
B) Type II error because the building was built.
C) Type I error because the building was built, but it was not profitable.
D) Type II error because the building was built and was profitable.

Question 30

Using R, what function is used to denote the hypothesized value of the mean?

A) alternative
B) option conf.
C) t.test
D) mu

Question 31

In a sample of 530 students, 80% prefer online resources versus printed materials. The standard error for the sample proportion is

A) 0.003
B) 0.017
C) 0.013
D) 0.040

Question 32

In a sample of 500 students, 80% prefer online resources versus printed materials. The standard error for the sample proportion is

A) 0.002
B) 0.018
C) 0.014
D) 0.040

Question 33

Which one of the following is not a characteristic of t distribution?

A) t distribution is defined by the degrees of freedom.
B) t distribution is bell-shaped.
C) t distribution is symmetric along zero.
D) t distribution is commonly known as population mean.

Question 34

According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,438 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 45 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,550 square feet with a sample standard deviation of 54 square feet. What are the competing hypotheses?

A) H₀: $\mu$ $\neq$ 2,438;H_A $\mu$ = 2,438
B) H₀: $\mu$ $\neq$ 1,550; H_A $\mu$ = 1,550
C) H₀: $\mu$ $\ge$ 2,438; H_A $\mu$ < 2,438
D) H₀: $\mu$ = 1,550; H_A $\mu$ $\neq$ 1,550

Question 35

According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,431 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 67 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,390 square feet with a sample standard deviation of 65 square feet. Calculate the value of the test statistic.

A) -0.83
B) 1.82
C) -1.96
D) 0.83

Question 36

According to the United States Census Bureau, the average single-family home constructed in 2016 was 2,438 square feet. Carmen wondered if families in her area still want a smaller home in comparison to the average. She randomly selected 45 people and asked what the ideal square footage of a home is for them. From the responses, she calculated the sample mean equals 1,550 square feet with a sample standard deviation of 54 square feet. Calculate the value of the test statistic.

A) -110.32
B) 110.54
C) -2.45
D) 1.32

Question 37

If t₃₄ = -4.322 and ? = 0.05, then what is the approximate of the p-value for a left-tailed test?

A) P(T₃₄ $\le$ -4.322) < 0.005.
B) P(T₃₄ $\le$ -4.322) < 0.05.
C) P(T₃₄ $\ge$ - 4.322) < 0.05.
D) P(T₃₄ $\ge$ 4.322) < 0.50.

Question 38

What does $\alpha$ = 0.01 reflect?

A) There is a 1% chance of rejecting a true null hypothesis.
B) There is a 1% chance of accepting a true null hypothesis.
C) Without an identified $\mu$ , there is no significant meaning.
D) The 1% is the highest significance level.

Question 39

In a World Atlas study, 10% of people have blue eye color. Lane decided to observe 35 people and she concluded 6 people had blue eyes. Calculate the z-score.

A) 0.1714
B) 0.0710
C) 1.4086
D) 0.5675

Question 40

In a World Atlas study, 10% of people have blue eye color. Lane decided to observe 35 people and she concluded 5 people had blue eyes. Calculate the z-score.

A) 0.1428
B) 0.0430
C) 0.8452
D) 0.0041

Question 41

In a 2019 Quinnipiac University poll of registered voters, 52% oppose making all U.S public colleges free. The Glangariff Group in Michigan collected data from 600 voters, where 342 support a taxpayer-funded free college program. What is the competing hypothesis?

A) H₀:p = 0.52; H_A:p $\neq$ 0.52
B) H₀ = 0.51; HA $\neq$ 0.51
C) H₀:p = 0.51; H_A:p $\neq$ 0.51
D) H₀:p = 0.57; H_A:p $\neq$ 0.57

Question 42

In a 2019 Quinnipiac University poll of registered voters, 58% oppose making all U.S public colleges free. The Glangariff Group in Michigan collected data from 610 voters, where 375 support a taxpayer-funded free college program. Calculate the value of the test statistic.

A) 1.38
B) 1.74
C) 11.31
D) 1.33

Question 43

In a 2019 Quinnipiac University poll of registered voters, 52% oppose making all US public colleges free. The Glangariff Group in Michigan collected data from 600 voters, where 342 support a taxpayer-funded free college program. Calculate the value of the test statistic.

A) 2.09
B) 2.45
C) 12.02
D) 2.04

Question 44

A p-value of 0.07698 was reported for a study with a 10% significance level. Should the null hypothesis be accepted or rejected?

A) Accept the null hypothesis because the p-value = 0.07698 is part of $\alpha$ = 0.10
B) Accept the null hypothesis because the p-value = 0.07698 is less than $\alpha$ = 0.10
C) Reject the null hypothesis because the p-value = 0.07698 is less than $\alpha$ = 0.10
D) Not enough information to determine.

Question 45

Many sample sizes can be drawn from a population, but there is only one overall population.

Question 46

The value of the sample mean will remain static even when the data set from the population is changed.

Question 47

<p>The sampling distribution of ^P is closely related to the normal distribution.< / p>

Question 48

In general, a normal distribution approximation is justified for the sample proportion when np $\ge$ 5 and n (1 - p) $\ge$ 5.

Question 49

The more degrees of freedom, the broader the tails of the distribution.

Question 50

With a df = 20, and $\alpha$ = 0.05 and a referencing table value of 1.74742, the upper tail suggests that P(T₂₀ $\ge$ 1.74742) = 0.05.

Question 51

The population proportion p is the essential measure for a quantitative variable.

Question 52

An alternative hypothesis, denotedH_A , is defined as the contradiction of the default state or status quo.

Question 53

In performing a test statistic for p, the formula is only valid if ^P </em> (approximately) follows a normal distribution.</ p>