MC Chapter 27 – Inference on slope

Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, five different doses of growth hormone (0, .2, .4, .8, and 1.0 mg/kg) were injected into chickens (three for each dose) and the subsequent weight gain was recorded. An experimenter plots the data and finds that a linear relationship appears to hold. A computer output follows:

SOURCE DF SUM OF SQUARES MEAN SQUARE F VALUE p-value MODEL 1 78.4083 78.4083 8.11 .0137ERROR 13 125.7410 9.6723TOTAL 14 204.1493

COEFFICENT StDev T p CONSTANT 3.7816 1.1705 3.23 0.0066 DOSE 4.0416 1.4195 2.85 0.01371) The least-squares regression line is:

yA) = 4.04 + 3.78x B) = 3.23 + 2.85x C) = 2.85 + 3.23x

E) = 1.17 + 1.42x

y y

yyD) = 3.78 + 4.04x

Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, five different doses of growth hormone (0, .2, .4, .8, and 1.0 mg/kg) were injected into chickens (three for each dose) and the subsequent weight gain was recorded. An experimenter plots the data and finds that a linear relationship appears to hold. A computer output follows:

SOURCE DF SUM OF SQUARES MEAN SQUARE F VALUE p-value MODEL 1 78.4083 78.4083 8.11 .0137ERROR 13 125.7410 9.6723TOTAL 14 204.1493

COEFFICENT StDev T p CONSTANT 3.7816 1.1705 3.23 0.0066 DOSE 4.0416 1.4195 2.85 0.01372) A 95% confidence interval for the slope is:

A) 4.04±1.96(1.42) B) 4.04±1.77(1.42)

D) 3.78±1.77(1.17) E) 3.78±2.16(1.17)

C) 4.04±2.16(1.42)

Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, five different doses of growth hormone (0, .2, .4, .8, and 1.0 mg/kg) were injected into chickens (three for each dose) and the subsequent weight gain was recorded. An experimenter plots the data and finds that a linear relationship appears to hold. A computer output follows:

SOURCE DF SUM OF SQUARES MEAN SQUARE F VALUE p-value MODEL 1 78.4083 78.4083 8.11 .0137ERROR 13 125.7410 9.6723TOTAL 14 204.1493

COEFFICENT StDev T p CONSTANT 3.7816 1.1705 3.23 0.0066 DOSE 4.0416 1.4195 2.85 0.01373) It is suspected that weight gain should increase with dose. An appropriate null and alternate hypothesis to test the slope, the test statistic, and the p-value are:

A) H0: = 0 Ha: < 0; T = 2.85; p-value = .0069 B) H0 : 0 Ha: < 0; T = 3.23; p-value = .0066 C) H0: = 0 Ha: > 0; T = 2.85; p-value = .0137 D) H0: = 0 Ha: > 0; T = 3.23; p-value = .0033 E) H0: = 0 Ha: > 0; T = 2.85; p-value = .0069

4) A large sample hypothesis test with σ known of a null hypothesis μ = 15 against the alternative hypothesis μ ≠ 15 results in the test statistic value of z = 1.37. Assuming σ is known, the corresponding p-value is approximately

A) 0.0853

C) 0.4147 D) 0.8293

E) 0.9147

B) 0.1707

5) Given the data below, in conducting a test of association between gender and grade, what is the expected count for the number of males who earned a grade of B?

A B C D

Male 10 32 25 6

Female 5 41 14 12

A) 32.5 B) 35.5

D) 41.0 E) It cannot be determined

C) 36.8

6) In a sample survey of 450 residents of a given community, 180 of them indicated that they shop at the local mall at least once per monthly. Construct a 95% confidence interval to estimate the true percentage of residents who shop monthly at the local mall.

B) (0.366, 0.434)

C) (0.377, 0.423) D) (0.380, 0.420)

E) It cannot be determined from the information given

A) (0.355, 0.445)

7) The table below shows the probability distribution for the number of tails (X) in five tosses of a fair coin. What is μx?

X 0 1 2 3 4 5

P(X) .03125 .15625 .3125 .3125 .15625 .03125

A) 2.0

C) 3.0 D) 3.5

E) 4.0

B) 2.5

8) A regression line includes the point (2, 14) and has the equation

= mx+4. If and are the sample means of the x and y values,

then =

y x y

y

x

A)

C) D)

E)

1

7x

4x

2x

5 4x B)

9) Failing to reject a null hypotheses that is false can be characterized as

A) a Type I error

C) both a Type I and Type II error

D) A standard error of the mean

E) No error

B) a Type II error

10) The probability of a tourist visiting an area cave is 0.70 and of a tourist visiting a nearby park is 0.60. The probability of visiting both places on the same day is 0.40. The probability that a tourist visits at least one of these two places is

A) 0.08 B) 0.28

C) 0.42

E) 0.95

D) 0.90

1)D 2) C

3) E 4) B

5) C 6) A

7) B 8) B

9) B 10) D