Question 1

A test was made of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 }$ The sample means $\bar { x } _ { 1 } = 7$ and $\bar { x } _ { 2 } = 13$ the sample standard deviations were $s _ { 1 } = 7 \text { and } s _ { 2 } = 5$ and the sample sizes
were $n _ { 1 } = 18 \text { and } n _ { 2 } = 16$
Compute the value of the test statistic.

Accepted Answer

A)  -0.697 
B)  -4.067 
C)  -7.164 
D)  -2.899

Question 2

The bowling scores of a professional bowler during a two-day tournament are shown below

Can you conclude that the variability of the scores is greater on the second day than on thi first day? Use the $\alpha = 0.01$ level of significance.

Accepted Answer

A) True 
 B)False

Question 3

The football coach at State University wishes to determine if there is a decrease in offensive production between the first half and the second half of his team's recent games. The table below shows the first-half and second-half offensive production (measured in total yards gained per half) for the past six games.
 $\begin{array}{lcccccc}
\hline &{\text { Game }} \
 & 1 & 2 & 3 & 4 & 5 & 6 \
 \text { First half yards } & 142 & 143 & 85 & 84 & 138 & 71 \
\text { Second half yards } & 134 & 116 & 66 & 84 & 122 & 65 \
\hline
\end{array}$

Compute the test statistic.

Accepted Answer

A)  $3.165$ 
B)  $2.881$ 
C)  $1.288$ 
D)  $9.895$

Question 4

An automobile manufacturer wishes to test that claim that synthetic motor oil can improve gas mileage (in miles per gallon, or mpg). The table below shows the gas mileages, in mpg, of six cars that used synthetic motor oil. The table also shows the gas mileages in mpg of six cars that were using conventional motor oil (the controls).
 $\begin{array}{rrrrrrr}
\hline \text { Synthetic: } & 27 & 27 & 26 & 27 & 27 & 29 \
\text { Control: } & 25 & 25 & 25 & 26 & 27 & 25 \
\hline
\end{array}$
Can you conclude that the mean gas mileage for cars using synthetic motor oil is more than the mean for the controls? Use the $\alpha = 0.05$ level of significance.

Accepted Answer

A) True 
 B)False

Question 5

In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land were treated with fertilizer A, and 10 randomly selected plots were treated with fertilizer B. The The number of pounds of harvested fruit was measured from each plot. Following are the results.
 $\begin{array}{lllllll}
{\text { Fertilizer A }} \
\hline 448 & 478 & 482 & 442 & 455 & 480 & 457 \
\hline 506 & 470 & 444 & 466 & 427 & 461 & 431 \
\hline
\end{array}$

$\begin{array}{ccccc}
{\text { Fertilizer B }} \
\hline 436 & 478 & 453 & 489 & 400 \
\hline 444 & 495 & 438 & 481 & 501
\end{array}$
Assume that the populations are approximately normal. Can you conclude that there is a difference in the mean yields for the two types of fertilizer? Use the $\alpha = 0.01$ level of significance.

Accepted Answer

A) True 
 B)False

Question 6

In a test for the difference between two proportions, the sample sizes were $n _ { 1 } = 88$ and $n _ { 2 } = 84$ and the numbers of events were $x _ { 1 } = 34 \text { and } x _ { 2 } = 39$ A test is made of the hypothesis $H _ { 0 } : p _ { 1 } = p _ { 2 } \text { versus } H _ { 1 } : p _ { 1 } \neq p _ { 2 }$ Can you reject $H _ { 0 }$ rejected at the $\alpha = 0.05$ level?

Accepted Answer

A) True 
 B)False

Question 7

A amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.
She hits fourteen balls with driver A and 10 balls with driver B. The The drive distances (in yards) for the trials are show below
$\text { Driver A }$ 
$\begin{array}{lllllll}
\hline 265 & 278 & 299 & 314 & 243 & 248 & 275 \
\hline 276 & 265 & 266 & 277 & 248 & 276 & 282 \
\hline
\end{array}$

$\begin{array}{lllll}
{\text { Driver B }} \
\hline 233 & 220 & 217 & 239 & 235 \
\hline 245 & 261 & 194 & 272 & 233 \
\hline
\end{array}$
Assume that the populations are approximately normal. Can you conclude that there is a difference in the mean drive distances for the two drivers? Use the $\alpha = 0.05$ level of significance.

Accepted Answer

A) True 
 B)False

Question 8

A garden seed wholesaler wishes to test the claim that tomato seeds germinate faster when each individual seed is "pelletized" within a coating of corn starch. The table below shows the germination times, in days, of six pelletized seeds. The table also shows the germination times in days of six un-coated seeds (the controls).
$\begin{array}{rrrrrrr}
\hline \text { Pelletized: } & 9 & 9 & 9 & 8 & 7 & 8 \
\text { Control: } & 9 & 10 & 11 & 13 & 9 & 11 \
\hline
\end{array}$
Can you conclude that the mean germination time for pelletized seeds is less than the mean for the un-pelletized seeds? Use the $\alpha = 0.05$ level of significance.

Accepted Answer

A) True 
 B)False

Question 9

The following MINITAB output display presents the results of a hypothesis test for the difference $\mu _ { 1 } - \mu _ { 2 }$ between two population means.
$\begin{array}{l}
\text { Two-sample T for X1 vs X2 }\
\begin{array}{rrrrc} 
& \mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } \
\text { A } & 7 & 112.415 & 23.485 & 8.876 \
\text { B } & 8 & 122.788 & 23.222 & 8.210
\end{array}
\end{array}$

Difference $= \operatorname { mu } ( \mathrm { X } 1 ) - \mathrm { mu } ( \mathrm { X } 2 )$
Estimate for difference: $- 10.373$
$95 \%$ CI for difference: $( - 34.072,13.326 )$
T-Test of difference $= 0 ($ vs not $= ) :$ T-Value $= - 0.857889$
$\mathrm { P }$-Value $= 0.406493 \quad \mathrm { DF } = 13$
Can you reject $H _ { 0 }$ rejected at the $\alpha = 0.10$ level?

Accepted Answer

A) True 
 B)False

Question 10

In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data were obtained:

Can you conclude that the mean weight differs between the two balances?
i). State the null and alternative hypotheses.
ii). Compute the test statistic.
iii). State a conclusion using the α = 0.02 level of significance.

Accepted Answer

The answer of In an experiment to determine whether there...

Question 11

In a test for the difference between two proportions, the sample sizes were $n _ { 1 } = 84$ and $n _ { 2 } = 102$ and the numbers of events were $x _ { 1 } = 35 \text { and } x _ { 2 } = 64$ A test is made of the hypothesis $H _ { 0 } : p _ { 1 } = p _ { 2 } \text { versus } H _ { 1 } : p _ { 1 } \neq p _ { 2 }$
Compute the value of the test statistic.

Accepted Answer

A)   -2.87 
B)   -2.80 
C)   -2.93 
D)   -2.70

Question 12

The football coach at State University wishes to determine if there is a decrease in offensive production between the first half and the second half of his team's recent games. The table below shows the first-half and second-half offensive production (measured in total yards gained per half)
for the past six games.
 $\begin{array}{lcccccc}
\hline &{\text { Game }} \
& 1 & 2 & 3 & 4 & 5 & 6 \
 \text { First half yards } & 99 & 127 & 131 & 106 & 112 & 144 \
\text { Second half yards } & 89 & 111 & 129 & 92 & 103 & 137 \
\hline
\end{array}$

State a conclusion using the $\alpha = 0.02$ level of significance.

Accepted Answer

A)  Reject $H _ { 0 }$. The mean offensive production appears to decrease from the first half to the second half. 
B)  Do not reject $H _ { 0 }$. There is insufficient evidence to conclude that the mean offensive production decreases from the first to the second half.

Question 13

In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data were obtained:
$\begin{array}{crr}
\hline \text { Specimen } & {\mathrm{A}} & {\mathrm{B}} \
\hline 1 & 14.86 & 14.83 \
2 & 9.44 & 9.41 \
3 & 11.99 & 11.99 \
4 & 9.27 & 9.26 \
5 & 6.13 & 6.13 \
6 & 13.78 & 13.76 \
\hline
\end{array}$

Compute the test statistic.

Accepted Answer

A)  $0.313$ 
B)  $2.433$ 
C)  $1.083$ 
D)  $2.666$

Question 14

A study reported that in a sample of 81 men, 25 had elevated total cholesterol levels (more than 200 milligrams per deciliter). In a sample of 99 women, 34 had elevated cholesterol levels.
Can you conclude that the proportion of people with elevated cholesterol levels differs between men and women? Use the $\alpha = 0.05$ level of significance.

Accepted Answer

A) True 
 B)False

Question 15

he following MINITAB output display presents the results of a hypothesis test on the difference between two proportions.
Test and CI for Two Proportions: P1, P2
$\begin{array} { l r r c } \text { Variable } & \mathrm { X } & \mathrm { N } & \text { Sample P } \ \text { P1 } & 47 & 109 & 0.431193 \ \text { P2 } & 40 & 96 & 0.416667 \end{array}$
Difference $= \mathrm { p } ( \mathrm { P } 1 ) = \mathrm { p } ( \mathrm { P } 2 )$
Estimate for differencę.014526
$95 \%$ CI for difference:(-0.121065, 0.150117)
T-Test of difference $= 0 ($ vs not $= \not ) = 0.209977$ P-Value $= 0.833686$ Is this a left-tailed test, a right-tailed test, or a two tailed test?

Accepted Answer

A) Two-tailed test 
B) Left-tailed test 
C) Right-tailed test

Question 16

The following MINITAB output display presents the results of a hypothesis test for the difference $\mu _ { 1 } - \mu _ { 2 }$ between two population means.
$\begin{array}{l}
\text { Two-sample T for X1 vs X2 }\
\begin{array}{rrrrc} 
& \mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } \
\text { A } & 15 & 71.319 & 24.905 & 6.430 \
\text { B } & 15 & 50.450 & 24.951 & 6.442
\end{array}
\end{array}$

Difference $= \operatorname { mu } ( \mathrm { X } 1 ) - \mathrm { mu } ( \mathrm { X } 2 )$
Estimate for difference: $20.869$
$95 \%$ CI for difference: $( 3.028,38.710 )$
T-Test of difference $= 0 ($ vs not $= ) :$ T-Value $= 2.292686$
P-Value $= 0.029586 \quad$ DF $= 28$
How many degrees of freedom are there for the test statistic?

Accepted Answer

A)  27 
B)   0.029586 
C)  28 
D)   20.869

Question 17

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for the difference between two means. The sample sizes are  $n _ { 1 } = 7 \text { and } n _ { 2 } = 15$

Can you reject  $H _ { 0 }$  rejected at the $\alpha = 0.05$ level?

Accepted Answer

A) True 
 B)False

Question 18

Following is a sample of five matched pairs. 
 $\begin{array}{llllll}
\hline \text { Sample 1 } & 15 & 21 & 14 & 17 & 24 \
\text { Sample } 2 & 22 & 16 & 20 & 14 & 20 \
\hline
\end{array}$

Let $\mu _ { 1 }$ and $\mu _ { 2 }$ represent the population means and let $\mu _ { \mathrm { d } } = \mu _ { 1 } - \mu _ { 2 }$. A test will be made of the hypotheses $H _ { 0 } : \mu _ { \mathrm { d } } = 0$ versus $H _ { 1 } : \mu _ { \mathrm { d } } > 0$. Compute the test statistic.

Accepted Answer

A)  $- 0.186$ 
B)  $- 0.077$ 
C)  $- 0.034$ 
D)  $- 0.089$

Question 19

A test was made of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 }$
The sample means were $\bar { x } _ { 1 } = 14$ and $\bar { x } _ { 2 } = 11 \text {, }$ the sample standard deviations were $s _ { 1 } = 8 \text { and } s _ { 2 } = 4$ and the sample sizes were $n _ { 1 } = 12 \text { and } n _ { 2 } = 20$
How many degrees of freedom are there for the test statistic, using the simple method?

Accepted Answer

A)  12 
B)  11 
C)  13 
D)  10

Exam 11: Correlation and Regression

The bowling scores of a professional bowler during a two-day tournament are shown below Can you conclude that the variability of the scores is greater on the second day than on thi first day? Use the α=0.01\alpha = 0.01α=0.01 level of significance.