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Chapter 8: Q27E (page 478)

A paired difference experiment yielded ndpairs of observations. In each case, what is the rejection region for testing H0:渭d>2?

a. nd=12,伪=.05

b.nd=24,伪=.10

c.nd=4,伪=.025

d.nd=80,伪=.01

Short Answer

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Checking items and paperwork to assess how well demands or criteria are satisfied, finding flaws, measuring excellence as well as danger, establishing trust, and preventing problems.

Step by step solution

01

Step-by-Step Solution Step 1: (a) State the rejection region when  nd= 12, α = 0.05

For a small sample size, the rejection criteria will depend upon the t-test.

Here, n=12

So, the degree of freedom will be n-1=11

伪=0.05

So, the upper-tailed test rejection region will be t>1.796

02

(b) State the rejection region when nd= 24, α = 0.10

For a small sample size, the rejection criteria will depend upon the t-test.

Here, n=24

So, the degree of freedom will be n-1=23

伪=0.10

So, the upper-tailed test rejection region will be t>1.319
03

(c) State the rejection region when nd= 4, α = 0.025

For a small sample size, the rejection criteria will depend upon the t-test.

Here, n=4

So, the degree of freedom will be n-1=3

伪=0.025

So, the upper-tailed test rejection region will be t>3.181

04

(d) State the rejection region when nd= 80, α = 0.01

For a large sample size, the rejection criteria will depend upon the t-test.

Here,n=80

So, the degree of freedom will be =n鈭�1=79

伪=0.01

So, the upper-tailed test rejection region will bet>2.374

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Most popular questions from this chapter

The 鈥渨inner鈥檚 curse鈥� in transaction bidding. In transaction bidding, the 鈥渨inner鈥檚 curse鈥� is the miracle of the winning (or loftiest) shot price being above the anticipated value of the item being auctioned. The Review of Economics and Statistics (Aug. 2001) published a study on whether shot experience impacts the liability of the winner鈥檚 curse being. Two groups of a stab in a sealed-shot transaction were compared (1)super-experienced stab and (2) less educated stab. In the super-experienced group, 29 of 189 winning flings were above the item鈥檚 anticipated value; 32 of 149 winning flings were above the item鈥檚 anticipated value in the less-educated group.

  1. Find an estimate of p1, the true proportion of super educated stab who fell prey to the winner鈥檚 curse
  2. Find an estimate of p2, the true proportion of less-educated stab who fell prey to the winner鈥檚 curse.
  3. Construct a 90 confidence interval for p1-p2.
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Question: Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise 6.29 (p. 348). Recall that the variable of interest was the average distance separating traps鈥攃alled trap-spacing鈥攄eployed by teams of fishermen. The trap-spacing measurements (in meters) for a sample of seven teams from the Bahia Tortugas (BT) fishing cooperative are repeated in the table. In addition, trap-spacing measurements for eight teams from the Punta Abreojos (PA) fishing cooperative are listed. For this problem, we are interested in comparing the mean trap-spacing measurements of the two fishing cooperatives.

BT Cooperative

93

99

105

94

82

70

86

PA Cooperative

118

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72

90

66

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Source: Based on G. G. Chester, 鈥淓xplaining Catch Variation Among Baja California Lobster Fishers Through Spatial Analysis of Trap-Placement Decisions,鈥� Bulletin of Marine Science, Vol. 86, No. 2, April 2010 (Table 1).

a. Identify the target parameter for this study.b. Compute a point estimate of the target parameter.c. What is the problem with using the normal (z) statistic to find a confidence interval for the target parameter?d. Find aconfidence interval for the target parameter.e. Use the interval, part d, to make a statement about the difference in mean trap-spacing measurements of the two fishing cooperatives.f. What conditions must be satisfied for the inference, part e, to be valid?

Independent random samples from normal populations produced the results shown in the next table.

Sample 1


Sample 2

1.23.11.72.83.0

 4.22.73.63.9

a. Calculate the pooled estimate of 蟽2.

b. Do the data provide sufficient evidence to indicate that 渭2&驳迟;渭1? Test using 伪=.10.

c. Find a 90% confidence interval for (渭1鈭�渭2).

d. Which of the two inferential procedures, the test of hypothesis in part b or the confidence interval in part c, provides more information about (渭1鈭�渭2)?

Question: Impact of race on football card values. Refer to the Electronic Journal of Sociology (2007) study of the Impact of race on the value of professional football players鈥� 鈥渞ookie鈥� cards, Exercise 12.72 (p. 756). Recall that the sample consisted of 148 rookie cards of NFL players who were inducted into the Football Hall of Fame (HOF). The researchers modelled the natural logarithm of card price (y) as a function of the following independent variables:

Race:x1=1ifblack,0ifwhiteCardavailability:x2=1ifhigh,0iflowCardvintage:x3=yearcardprintedFinalist:x4=naturallogarithmof鈥�numberoftimesplayeron鈥�finalHOFballotPosition-QB::x5=1ifquarterback,0ifnotPosition-RB:x7=1ifrunningback,0ifnotPosition-WR:x8=1ifwidereceiver,0ifnotPosition-TEx9=1iftightend,0ifnotPosition-DL:x10=1ifdefensivelineman,0ifnotPosition-LB:x11=1iflinebacker,0ifnotPosition-DB:x12=1ifdefensiveback,0ifnot

[Note: For position, offensive lineman is the base level.]

  1. The model E(y)=尾0+尾1x1+尾2x2+尾3x3+尾4x4+尾5x5+尾6x6+尾7x7+尾8x8+尾9x9+尾10x10+尾11x11+尾12x12 was fit to the data with the following results:R2=0.705,Ra2=0.681,F=26.9.Interpret the results, practically. Make an inference about the overall adequacy of the model.
  2. Refer to part a. Statistics for the race variable were reported as follows:尾^1=-0.147,s尾^1=-0.145,t=-1.014,p-value=0.312 .Use this information to make an inference about the impact of race on the value of professional football players鈥� rookie cards.
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  4. Write a first-order model for E(y) as a function of card vintage x3and position x5-x12that allows for the relationship between price and vintage to vary depending on position.

Question: Forecasting daily admission of a water park. To determine whether extra personnel are needed for the day, the owners of a water adventure park would like to find a model that would allow them to predict the day鈥檚 attendance each morning before opening based on the day of the week and weather conditions. The model is of the form

where,

y = Daily admission

x1 = 1 if weekend

0 otherwise

X2 = 1 if sunny

0 if overcast

X3 = predicted daily high temperature (掳F)

These data were recorded for a random sample of 30 days, and a regression model was fitted to the data.

The least squares analysis produced the following results:

with

  1. Interpret the estimated model coefficients.
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  3. Is there sufficient evidence to conclude that the mean attendance increases on weekends? Use 伪 = .10.
  4. Use the model to predict the attendance on a sunny weekday with a predicted high temperature of 95掳F.
  5. Suppose the 90% prediction interval for part d is (645, 1,245). Interpret this interval.
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