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Dilini chathurthi

Dilini c.

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State (a) a positive economic statement of your choice, and then (b) a normative cconomic statement relating to your first statement. LO2

State (a) a positive economic statement of your choice, and then (b) a normative cconomic statement relating to your first statement. LO2

Economics Principles, Problems, and Policies

Use the given data to find the minimum sample size required to estimate a population proportion or percentage.
You are the operations manager for American Airlines and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage of passengers who now prefer aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be $95 \%$ confident that the sample percentage is within
2.5 percentage points of the true population percentage.
a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.
b. Assume that a prior survey suggests that about $38 \%$ of air passengers prefer an aisle seat (based on a $3 \mathrm{M}$ Privacy Filters survey).

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. You are the operations manager for American Airlines and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage of passengers who now prefer aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be $95 \%$ confident that the sample percentage is within 2.5 percentage points of the true population percentage. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. b. Assume that a prior survey suggests that about $38 \%$ of air passengers prefer an aisle seat (based on a $3 \mathrm{M}$ Privacy Filters survey).

Elementary Statistics

Estimating Parameters and Determining…

Estimating a Population Proportion

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 474 eggs in group I boxes, of which a field count showed about 270 had hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 805 eggs in group II boxes, of which a field count showed about 270 had hatched.
(a) Find a point estimate $\hat{p}_{1}$ for $p_{1},$ the proportion of $\mathrm{cggs}$ that hatched in group I nest box placements. Find a $95 \%$ confidence interval for $p_{1}$
(b) Find a point estimate $\hat{p}_{2}$ for $p_{2},$ the proportion of eggs that hatched in group II nest box placements. Find a $95 \%$ confidence interval for $p_{2}$
(c) Find a $95 \%$ confidence interval for $p_{1}-p_{2} .$ Does the interval indicate that the proportion of eggs hatched from group I nest boxes is higher than, lower than, or equal to the proportion of eggs hatched from group II nest boxes?
(d) What conclusions about placement of nest boxes can be drawn? In the article discussed in the Focus Problem, additional concerns are raised about the higher cost of placing and maintaining group I nest box placements. Also at issue is the cost efficiency per successful wood duck hatch.

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 474 eggs in group I boxes, of which a field count showed about 270 had hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 805 eggs in group II boxes, of which a field count showed about 270 had hatched. (a) Find a point estimate $\hat{p}_{1}$ for $p_{1},$ the proportion of $\mathrm{cggs}$ that hatched in group I nest box placements. Find a $95 \%$ confidence interval for $p_{1}$ (b) Find a point estimate $\hat{p}_{2}$ for $p_{2},$ the proportion of eggs that hatched in group II nest box placements. Find a $95 \%$ confidence interval for $p_{2}$ (c) Find a $95 \%$ confidence interval for $p_{1}-p_{2} .$ Does the interval indicate that the proportion of eggs hatched from group I nest boxes is higher than, lower than, or equal to the proportion of eggs hatched from group II nest boxes? (d) What conclusions about placement of nest boxes can be drawn? In the article discussed in the Focus Problem, additional concerns are raised about the higher cost of placing and maintaining group I nest box placements. Also at issue is the cost efficiency per successful wood duck hatch.

Understandable Statistics, Concepts and Methods

Estimation

Estimating $\mu_{1}-\mu_{2}$ and…

Preliminary data analyses and other information indicate that you can reasonably assume that, the variable under consideration is normally distributed on both populations. For each exercise, use either the critical-value approach or the $P$-value approach to perform the required hypothesis test.
During the 1960 s, liquor stores either were run by the state as a monopoly or were privately owned. Independent samples of state-run and privately owned liquor stores yielded the following prices, in dollars, for a fifth of Seagram's 7 Crown Whiskey. [SOURCE: Julian L. Simon and Peter Bruce, "Resampling: A Tool for Everyday Statistical Work," Chance, Vol. 4(1), pp. 23-32]
$$\begin{array}{cccc|cccc}
\hline  {\text { State run }} &&&&  {\text { Privately owned }} \\
\hline 4.65 & 4.11 & 4.20 & 3.80 & 4.82 & 4.85 & 4.80 & 4.85 \\
4.74 & 4.10 & 5.05 & 4.00 & 4.54 & 5.20 & 4.90 & 4.29 \\
4.55 & 4.15 & 4.55 & 4.19 & 4.95 & 4.95 & 4.75 & 4.79 \\
4.50 & 4.00 & 4.20 & 4.75 & 5.29 & 4.85 & 4.29 & 4.85 \\
& & & & 4.75 & 5.10 & 5.25 & 4.95 \\
& & & & 4.75 & 4.55 & 4.79 & \\
& & 4.89 & 4.50 & 5.30 & \\
\hline
\end{array}$$
At the $10 \%$ significance level, do the data provide sufficient evidence to conclude that there was more price variation in staterun stores than in privately owned stores? (Note: $s_{1}=0.344$ and $\left.s_{2}=0.264 .\right)$

Preliminary data analyses and other information indicate that you can reasonably assume that, the variable under consideration is normally distributed on both populations. For each exercise, use either the critical-value approach or the $P$-value approach to perform the required hypothesis test. During the 1960 s, liquor stores either were run by the state as a monopoly or were privately owned. Independent samples of state-run and privately owned liquor stores yielded the following prices, in dollars, for a fifth of Seagram's 7 Crown Whiskey. [SOURCE: Julian L. Simon and Peter Bruce, "Resampling: A Tool for Everyday Statistical Work," Chance, Vol. 4(1), pp. 23-32] $$\begin{array}{cccc|cccc} \hline {\text { State run }} &&&& {\text { Privately owned }} \\ \hline 4.65 & 4.11 & 4.20 & 3.80 & 4.82 & 4.85 & 4.80 & 4.85 \\ 4.74 & 4.10 & 5.05 & 4.00 & 4.54 & 5.20 & 4.90 & 4.29 \\ 4.55 & 4.15 & 4.55 & 4.19 & 4.95 & 4.95 & 4.75 & 4.79 \\ 4.50 & 4.00 & 4.20 & 4.75 & 5.29 & 4.85 & 4.29 & 4.85 \\ & & & & 4.75 & 5.10 & 5.25 & 4.95 \\ & & & & 4.75 & 4.55 & 4.79 & \\ & & 4.89 & 4.50 & 5.30 & \\ \hline \end{array}$$ At the $10 \%$ significance level, do the data provide sufficient evidence to conclude that there was more price variation in staterun stores than in privately owned stores? (Note: $s_{1}=0.344$ and $\left.s_{2}=0.264 .\right)$

Introductory Statistics

Inferences for Population Standard…

Inferences for Two Population Standard…

Questions asked

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Andrew Davis verified

Numerade educator

Which of the following is incorrect? Select one: In a competitive market, buyers and sellers take the price as given A competitive market can have any number of buyers and sellers The market price and market quantity are determined by the interaction of consumers and producers A competitive market has many buyers and sellers

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Nick Johnson verified

Numerade educator

The minimum wage is an example of a Select one: Price ceiling that can cause a shortage Price ceiling that can cause a surplus Price floor that can cause a surplus Price floor that can cause a shortage

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Yujie Wang verified

Numerade educator

A company’s leading executive is:

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Prabhakar Kumar verified

Numerade educator

The Springfield Emergency Medical Service keeps records of emergency telephone calls. A study of 150 five-minute time intervals resulted in the distribution of number of calls as follows. For example, during 18 of the five-minute intervals, no calls occurred. Use the chi-square goodness-of-fit test and ? = .01 to determine whether this distribution is Poisson. Find the observed value of chi-square. Round the answer to 2 decimal places. Number of Calls (per 5-minute interval) Frequency 0 18 1 28 2 47 3 21 4 16 5 11 6 or more 9

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Lucas Finney verified

Numerade educator

The Springfield Emergency Medical Service keeps records of emergency telephone calls. A study of 150 five-minute time intervals resulted in the distribution of number of calls as follows. For example, during 18 of the five-minute intervals, no calls occurred. Use the chi-square goodness-of-fit test and ? = .01 to determine whether this distribution is Poisson. Find the observed value of chi-square. Round the answer to 2 decimal places. Number of Calls (per 5-minute interval) Frequency 0 18 1 28 2 47 3 21 4 16 5 11 6 or more 9

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Samriddhi Singh verified

Numerade educator

The general manager of an AFL team believes the ages of purchasers of game tickets are normally distributed. The following data represent the distribution of ages for a sample of observed purchasers of AFL game tickets. Use the chi-square goodness-of-fit test to determine whether this distribution is significantly different from the normal distribution. Assume that α = .05. Age of Purchaser Frequency 10–under 20 16 20–under 30 44 30–under 40 61 40–under 50 56 50–under 60 35 60–under 70 19 Round your answer to 4 decimal places when calculating using Table A.8. What is the p-value?

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Samriddhi Singh verified

Numerade educator

The general manager of an AFL team believes the ages of purchasers of game tickets are normally distributed. The following data represent the distribution of ages for a sample of observed purchasers of AFL game tickets. Use the chi-square goodness-of-fit test to determine whether this distribution is significantly different from the normal distribution. Assume that � = .9. Age of Purchaser Frequency 10–under 20 16 20–under 30 44 30–under 40 61 40–under 50 56 50–under 60 35 60–under 70 19 Round your answer to 4 decimal places when calculating using Table A.8. What is value?

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Paul A. verified

Numerade educator

Use a chi-square goodness-of-fit test to determine whether the following observed frequencies are distributed the same as the expected frequencies. Let ? = 0 .01 Find the observed value of chi-square. Round the answer to 2 decimal places. Category 1 214 206 2 235 232 3 279 268 4 281 284 5 264 268 6 254 232 7 211 206

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Qudsiya Anis verified

Numerade educator

The general manager of an AFL team believes the ages of purchasers of game tickets are normally distributed. The following data represent the distribution of ages for a sample of observed purchasers of AFL game tickets. Use the chi-square goodness-of-fit test to determine whether this distribution is significantly different from the normal distribution. Assume that � = .9. Age of Purchaser Frequency 10–under 20 16 20–under 30 44 30–under 40 61 40–under 50 56 50–under 60 35 60–under 70 19 Round your answer to 4 decimal places when calculating using Table A.8. What is value?

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Samriddhi Singh verified

Numerade educator

Two processes in a manufacturing line are performed manually: operation A and operation B. A random sample of 50 different assemblies using operation A shows that the sample average time per assembly is 8.05 minutes, with a population standard deviation of 1.36 minutes. A random sample of 38 different assemblies using operation B shows that the sample average time per assembly is 7.26 minutes, with a population standard deviation of 1.06 minutes. For α=.10, is there enough evidence in these samples to declare that operation A takes significantly longer to perform than operation B? Find the z-score to make a conclusion. Round the answer to two decimal places.

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