Mathematical Statistics with Applications
7th Edition
ISBN: 9781111798789
Author: Dennis O. Wackerly
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 12.2, Problem 6E
Refer to Exercise 12.5. Consider two methods for selecting the dosages. Method 1 assigns three rats to the dosage x = 2 and three rats to x = 5. Method 2 equally spaces the dosages between x = 2 and x = 5 (x = 2, 2.6, 3.2, 3.8, 4.4, and 5.0). Suppose that σ is known and that the relationship between E(Y) and x is truly linear (see Chapter 11). If we use the data from both methods to construct confidence intervals for the slope β1, which method will yield the longer interval? How much longer is the longer interval? If we use method 2, approximately how many observations will be required to obtain an interval the same length as that obtained by the optimal assignment of method 1?
12.5 Suppose that we wish to study the effect of the stimulant digitalis on the blood pressure Y of rats over a dosage
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The output of a solar panel (photovoltaic) system depends on its size. A manufacturer states that the average daily production of its 1.5 kW system is 6.6 kilowatt hours (kWh) for Perth conditions. A consumer group monitored this 1.5 kW system in 20 different Perth homes and measured the average daily production by the systems in these homes over a one month period during October. The data is provided here.
kWh 6.2, 5.8, 5.9, 6.1, 6.4, 6.3, 6.9, 5.5, 7.4, 6.7, 6.3, 6.2, 7.1, 6.8, 5.9, 5.4, 7.2, 6.7, 5.8, 6.9
1. Analyse the consumer group’s data to test if the manufacturer’s claim of an average of 6.6 kWh per day is reasonable. State appropriate hypotheses, assumptions and decision rule at α = 0.10. What conclusions would you report to the consumer group? (Hint: You will need to find Descriptive Statistics first.)
2. If 48 homes in the central Australian city of Alice Springs had this system installed and similar data was collected, in order to assess whether average daily production in…
2.An engineer at a semiconductor company wants to model the relationship between the
device HFE (y) and three parameters: Emitter-RS (x1), Base-RS (x2), and Emitter-to-
Base RS (x3). The data are shown in the following table.
X1
X2
X3
X1
X2
X3
y
14.620
226.000
7.000
128.400
15.500
230.200
5.750
97.520
15.630
220.000
3.375
52.620
16.120
226.500
3.750
59.060
14.620
217.400
6.375
113.900
15.130
226.600
6.125
111.800
15.000
220.000
6.000
98.010
15.630
225.600
5.375
89.090
14.500
226.500
7.625
139.900
15.380
229.700
5.875
101.000
15.250
224.100
6.000
102.600
14.380
234.000
8.875
171.900
16.120
220.500
3.375
48.140
15.500
230.000
4.000
66.800
15.130
223.500
6.125
109.600
14.250
224.300
8.000
157.100
15.500
217.600
5.000
82.680
14.500
240.500
10.870
208.400
15.130
228.500
6.625 112.600
14.620
223.700
7.375
133.400
(a) Fit a multiple linear regression model to the data.
(b) Predict HFE (y) when x1 =14.5, x2 = 220, and x3 = 5.0.
In the area of Russia récords were kept on the relationship between the rain Fall in inches and the yield of wheat (bushels per acre ).the data for a 9 year period is as follow.
Rain fall x 13.1,11.4,16.0,15.1,21.4,12.9,9.6,18.2,18.6.
yield y : 48.5,44.2,56.8,80.4,47.2,29.9,74.0,74.0,76.8
the equation of the line of least squares is given as ^y= -9.12+4.38x. How many bushels of wheat peen acre can be predicted if it’s is expected that there will be 30 inches of rain?
Chapter 12 Solutions
Mathematical Statistics with Applications
Ch. 12.2 - Suppose that you wish to compare the means for two...Ch. 12.2 - Refer to Exercise 12.1. Suppose that you allocate...Ch. 12.2 - Suppose, as in Exercise 12.1, that two populations...Ch. 12.2 - Refer to Exercise 12.3. How many observations are...Ch. 12.2 - Suppose that we wish to study the effect of the...Ch. 12.2 - Refer to Exercise 12.5. Consider two methods for...Ch. 12.2 - Refer to Exercise 12.5. Why might it be advisable...Ch. 12.2 - The standard error of the estimator 1 in a simple...Ch. 12.3 - Consider the data analyzed in Examples 12.2 and...Ch. 12.3 - Two computers often are compared by running a...
Ch. 12.3 - When Y1i, for i = 1, 2,, n, and Y2i, for i = 1,...Ch. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - A plant manager, in deciding whether to purchase a...Ch. 12.3 - Muck is the rich, highly organic type of soil that...Ch. 12.3 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Complete the assignment of treatments for the...Ch. 12 - Prob. 28SECh. 12 - Prob. 29SECh. 12 - Prob. 30SECh. 12 - Prob. 31SECh. 12 - Prob. 32SECh. 12 - Prob. 33SECh. 12 - Prob. 34SECh. 12 - The earths temperature affects seed germination,...Ch. 12 - An experiment was conducted to compare mean...Ch. 12 - Prob. 37SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardThe following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forward5. Consider the following two simple regression models: Model I : Y, = B,+B,X, +H, Model II : Y,=a, +a, (X,- X)+v, (1) Derive the estimators for B, and a,. Are they the same? (2) Derive the estimators for B, and a, . Are they the same?arrow_forward
- If u = x1x2 + x2x3+ X3X1, then find the relative percentage error in the computation of u at x1 = 2.104, x2 1.935 and x3= = 0.845.arrow_forwardSolve by hand calculations. Do not use any type of softwarearrow_forwardA sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia = 63.3 yr. 1 X,=65.2 yr. 2 o, = 9.1 yr. = 7.3 yr. n1 = 120 = 150arrow_forward
- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.5 8.5 7 3.7 2.7 2.5 2.6 0.8 yy 13.8 11.1 10.1 7.2 6.4 6.1 6.1 4.8 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation ˆy=0.85x+4.05.y^=0.85x+4.05. Use this equation to answer the following.A) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 3.3 thousand automatic weapons?Answer = Round to 3 decimal places.arrow_forwardConsider the following variables: Y=daily productivity score (measured in points) X1=0 if undergraduate student,1 if graduate student X2=hours of sleep per night 1. The plot shown below could possibly be the graph of which model? 2. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model should you consider and what is the null hypothesis for this test? 3. Suppose you use Model 5 to describe the relationship between type of student, hours of sleep per night, and daily productivity score. You use the method of least squares to obtain: Y = -0.5 + 3 (X1) + 1.5 (X2) + 2.5 (X1)(X2).arrow_forwardWe want to estimate the causal effect of D through regression, and S allows a perfect stratification. There are N stratums in S and we use Si to represent stratum i. If the estimated coefficient of Si*D is A and is significant, then the treatment effect of D for stratum i is A.arrow_forward
- Ww. 3.10® Expess 5 as a linear combination of and Voarrow_forwardWe are interested in using the pH of the lake water (which is easy to measure) to predict the average mercury level in fish from the lake, which is hard to measure. Let x be the pH of the lake water and Y be the average mercury level in fish from the lake. A sample of n = 10 lakes yielded the following data: Observation (i) pH (x;) Average mercury level (y;) 0.15 1 3 4 6 7 8 9 10 8.2 8.4 7.0 7.2 7.3 6.4 9.1 5.8 7.6 8.1 0.04 0.40 0.50 0.27 0.81 0.04 0.83 0.05 0.19 Suppose we fit the data with the following regression model: Y; = a + Bx; + Ei, i = 1, ..., 10, where ɛi ~ N (0, o?) are independent. We have the following quantities: a = E=1 ¤i = 7.51, j = E1 Yi = 0.328, 1 x = 572.71, 1 Y? = 1.8922, D-1 *iYi = 22.218. i=1 ri=1 Some R output that may help. > р1 qt (p1, 8) [1] -2.896 -2.306 -1.860 -1.397 1.397 1.860 2.306 2.896 > qt (p1, 9) [1] -2.821 -2.262 -1.833 -1.383 1.383 1.833 2.262 2.821 (a) Find the ordinary least squares (OLS) estimates (denoted as â and ß) of the regression…arrow_forwardFor b; for certain simple linear regression we have the following information: n=31 b; =1.26, 2(X,-X}= 530.45 SSE=1550.32, and t 0,025, 31=2.042, t 0.025, 29=2.045 or t 0.05, 29=1.699 then your deCision when alpha=01 is O a. For b1 =1.26, accept the null hypothesis, and there is no significant relationship between X and Y O b. For b1 =1.26, reject Ha, and there is no significant relationship between X and Y O c. For b1 =1.26, reject Ha, and there is a significant relationship between X and Y O d. For b1 =1.26, accept Ha, and there is a significant relationship between X and Yarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Introduction to experimental design and analysis of variance (ANOVA); Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=vSFo1MwLoxU;License: Standard YouTube License, CC-BY