Chapter 8, Hypothesis Testing Video Solutions, Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Problem 1

1. [C10] The number of terminals in use by Group Alfa during the lunch hour at Fairlady Aircraft is normally distributed. A random sample of 40 observed values of the number of active terminals is shown in the table. Assume $\sigma=5$. At the $5 \%$ level of significance, test the null hypothesis that the mean number of active terminals $\mu=20$ against the alternative hypothesis that $\mu>20$.
$$
\begin{array}{rrrr}
{\text { Random Sample }} \\
\hline & & & \\
22.5585 & 16.7495 & 19.8800 & 19.8130 \\
22.3250 & 23.2865 & 15.7555 & 11.8815 \\
24.5805 & 22.1430 & 30.7650 & 24.0120 \\
23.1480 & 16.2845 & 21.1555 & 22.1095 \\
19.0270 & 18.8885 & 24.2645 & 21.9145 \\
26.7180 & 27.4775 & 22.8960 & 14.3475 \\
18.3270 & 10.4450 & 27.1350 & 11.1425 \\
23.0950 & 26.8640 & 18.0160 & 9.9325 \\
21.5260 & 27.2705 & 21.5315 & 20.2230 \\
9.0565 & 18.7445 & 24.9890 & 17.7345 \\
\hline
\end{array}
$$

Vanna Tran

Numerade Educator

03:39

Problem 2

Fowler Heir Mining has selected the random sample of response times observed at the terminal used by the Vice President for Canaries. The values, in seconds, are shown in the table. Assuming the response times are normally distributed, test the null hypothesis that the mean response time $\mu=0.5$ seconds against the alternative hypothesis that $\mu>0.5$ seconds. Use the $5 \%$ level of significance.
$$
\begin{array}{llcll}
& & {\text { Random Sample at Fowler Heir }} \\
\hline & & & & \\
0.53 & 0.60 & 0.57 & 0.58 & 0.44 \\
0.68 & 0.49 & 0.55 & 0.51 & 0.59 \\
\hline
\end{array}
$$

Sheryl Ezze

Numerade Educator

00:32

Problem 3

The 200 programmers at Division A of Mickeysoft Corporation have averaged 76.21 lines of code per programmer-day with a sample standard deviation of 10.37 . The 150 programmers of Division B have averaged 72.72 lines with a sample standard deviation of 10.07. At the one percent level of significance, does it appear that the programmers of Division A are more productive than those of Division B?

Zach Steedman

Numerade Educator

01:24

Problem 4

Consider the situation of Exercise 3. Suppose it is discovered that the statistics gathered at Mickeysoft are based on only 6 programmers at Division A and 5 at division B. (The numbers are the same, though.) Assume the distribution of lines of code per programmer-day at both divisions is normally distributed with the same (unknown) mean. At the one percent level of significance, does it now appear that the programmers of Division A are more productive than those of Division B?

Sheryl Ezze

Numerade Educator

06:38

Problem 5

Consider Exercise 3. Assuming the distributions of lines of code per programmer-day are normal, test at the $10 \%$ level of significance the null hypothesis that the variances of lines of code per programmer-day are the same at the two divisions. Use the alternative hypothesis that they are different.

Erin Moser

Numerade Educator

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Problem 6

Consider Exercise 2. Assuming the response time distribution is normal, test at the $10 \%$ level of significance the null hypothesis that the variance $\sigma^2=0.004$. Use the alternative hypothesis that $\sigma^2>0.004$.

Victor Salazar

Numerade Educator

03:44

Problem 7

Badyere Tire claims that $90 \%$ of its Randy Radials last for more than 50,000 miles. Diligent Dealer wear tests ten Randy Radials and finds that two of them fail before 50,000 miles. Use Algorithm 8.4.2 to test the Badyere Tire claim at the $10 \%$ level of significance.

Charles Carter

Numerade Educator

03:14

Problem 8

Richilan Radials advertises that Richilan radial tires are better than Randy Radials. As proof, they tested 20 of their radials and 20 Randy Radials. Richilan claims that only 2 of their tires failed to reach 50,000 miles, but 7 Randy Radials failed. Use the Fisher-Irwin test at the $5 \%$ level of significance to test Richilan's claim. The null hypothesis is that there is no difference in the tires. The alternative hypothesis is that the fraction of good Richilan tires is higher than the fraction of good Randy tires.

Sheryl Ezze

Numerade Educator

01:37

Problem 9

Parsimonious Peripherals has developed a new $I / O$ device. The company claims that the table contains the retrieval times of 30 randomly selected $I / O$ requests. The times are in milliseconds. Parsimonious claims the processing times are normally distributed with a mean of 10 milliseconds and a standard deviation of 5 milliseconds. Test this claim using the chi-square test as follows. Normalize the data by the formula $z_i=\left(x_i-10\right) / 5$. Partition the real line into 5 intervals such that if $H_0$ is true, then one-fifth of the $z_i^{\prime} s$ would be expected in each interval. Apply the chi-square test with these intervals as cells. Use the $5 \%$ level of significance.
$$
\begin{array}{rrrrr}
{\text { Parsimonious Sample }} \\
\hline & & & & \\
14.560 & 4.102 & 7.514 & 8.873 & 10.373 \\
7.582 & 10.651 & 5.424 & 6.470 & 7.589 \\
3.022 & 8.666 & 1.966 & 17.381 & 15.564 \\
17.715 & 13.655 & 14.860 & 12.037 & 10.475 \\
5.298 & 9.750 & -1.371 & 7.274 & 14.901 \\
18.845 & 16.881 & 7.229 & 16.833 & 9.440 \\
\hline
\end{array}
$$

Qudsiya Anis

Numerade Educator

02:53

Problem 10

Whoopdedoo Fashions has taken a random sample of 15 communication line times of their interactive order entry system to yield the values in the table. (The units of time are druds.) Use the Kolmogorov-Smirnov test and the $A^2$ test to test the hypothesis that line time is exponential. Use the $10 \%$ level of significance.
$$
\begin{array}{rrrrr}
{\text { Whoopdedoo Fashions Sample }} \\
\hline & & & & \\
2.31 & 17.29 & 26.23 & 79.83 & 30.35 \\
3.59 & 1.29 & 0.58 & 4.81 & 15.87 \\
28.73 & 3.87 & 18.99 & 2.81 & 62.46 \\
\hline
\end{array}
$$

Sheryl Ezze

Numerade Educator

02:05

Problem 11

Consider the random sample of response times in Exercise 2. Use the Kolmogorov-Smirnov and $A^2$ tests at the $5 \%$ level to test the hypothesis that the response time is normally distributed. Assume the mean and variance are not known.

Lucas Finney

Numerade Educator

Problem 12

Without using the APL function CHISQ $\triangle$ EXPON, verify that the numbers for the chi-square test for exponentiality at the 5 percent level of significance quoted in Example 8.6.2 are correct.

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01:07

Problem 13

Consider Example 8.5.2. Suppose that for each World Series one team is more likely to win each game than the other. Assume the probability of winning each game is 0.6 for one team and 0.4 for the other team. Analyze the 50 games that we analyzed in Example 8.5.2, at the 5 percent level of significance.

Alexander Cheng

Numerade Educator

03:40

Problem 14

Silicon Valley Doodads has 4 computers in the central computer center that are run 3 shifts per day. Andy Exponential, the manager of the computer center, makes up the following contingency table, by computer and shift, of the number of times that the operators of a particular computer have been forced to do an IPL (initial program load) during the shift. Andy wants to test at the 5 percent level of significance whether the need for an IPL on a computer is independent of the computer and the shift. Please make the calculation for Andy.
$$
\begin{array}{l|r|r|r|r|r}
\hline {\text { Computer }} \\
\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Totals } \\
\hline \text { Shift 1 } & 5 & 3 & 2 & 7 & 17 \\
\text { Shift 2 } & 7 & 12 & 9 & 16 & 44 \\
\text { Shift 3 } & 1 & 2 & 4 & 2 & 9 \\
\hline \text { Totals } & 13 & 17 & 15 & 25 & 70 \\
\hline
\end{array}
$$

Andrew Kim

Numerade Educator

02:18

Problem 15

A consumer testing organization tests three brands of pickup trucks by crashing them into a barrier and recording the repair cost in dollars. Six vehicles of each type were tested. The results are recorded in the table below. Use one-way analysis of variance to test the hypothesis that the average damage to each brand of pickup is the same. Use the five percent level of significance.
$$
\begin{array}{r|r|r}
\hline & {\text { Pickup }} \\
\hline \text { Gorilla } & \text { Warrior } & \text { Gladiator } \\
\hline 200 & 75 & 120 \\
50 & 470 & 570 \\
150 & 20 & 600 \\
75 & 140 & 450 \\
100 & 220 & 700 \\
250 & 210 & 350 \\
\hline
\end{array}
$$

Sheryl Ezze

Numerade Educator

11:24

Problem 16

Solve Exercise 15 using the Kruskal-Wallis test.

Phumlani Ngcobo

Numerade Educator