Four different paints are advertised as having the same drying time. To check the manufacturer’s claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained.

$$\begin{matrix} \text{Paint 1} & \text{Paint 2} & \text{Paint 3} & \text{Paint 4}\\ \text{128} & \text{144} & \text{133} & \text{150}\\ \text{137} & \text{133} & \text{143} & \text{142}\\ \text{135} & \text{142} & \text{137} & \text{135}\\ \text{124} & \text{146} & \text{136} & \text{140}\\ \text{141} & \text{130} & \text{131} & \text{153}\\ \end{matrix}$$

At the $\alpha =$ .05 level of significance, test to see whether the mean drying time is the same for each type of paint.

Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800; SSTR = 4560. a. Set up the ANOVA table for this problem. b. Use $\alpha =$ .05 to test for any significant difference in the means for the three assembly methods.

Four different paints are advertised as having the same drying time. To check the manufacturer's claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained. At the $\alpha=.05$ level of significance, test to see whether the mean drying time is the same for each type of paint.

Four different paints are advertised as having the same drying time. To check the manufacturer’s claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained.

At the $\alpha$ = .05 level of significance, test to see whether the mean drying time is the same for each type of paint.

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker’s parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. During 2003, the overall mean SAT verbal score was 507 (The World Almanac, 2004). SAT verbal scores for independent samples of students follow. The first sample shows the SAT verbal test scores for students whose parents are college graduates with a bachelor’s degree. The second sample shows the SAT verbal test scores for students whose parents are high school graduates but do not have a college degree. Student's Parents

$$\begin{matrix} \text{College } & \text{Grads} && \text{High School} & \text{Grads}\\ \text{485} & \text{487} && \text{442} & \text{492}\\ \text{534} & \text{533} && \text{580} & \text{478}\\ \text{650} & \text{526} && \text{479} & \text{425}\\ \text{554} & \text{410} && \text{486} & \text{485}\\ \text{550} & \text{515} && \text{528} & \text{390}\\ \text{572} & \text{578} && \text{524} & \text{535}\\ \text{497} & \text{448}\\ \text{592} & \text{469}\\ \end{matrix}$$

Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean verbal score on the SAT if their parents attained a higher level of education.

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

$$\begin{matrix} \text{ } & \text{ } & \text{Language}\\ \text{ } & \text{Spanish} & \text{French} & \text{German}\\ \text{System 1} & \text{8} & \text{10} & \text{12}\\ \text{ } & \text{12} & \text{14} & \text{16}\\ \text{System 2} & \text{6} & \text{14} & \text{16}\\ \text{ } & \text{10} & \text{16} & \text{22}\\ \end{matrix}$$

Test for any significant differences due to language translator, type of language, and interaction. Use $\alpha =$ .05.

Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

$$\begin{array}{cc}\begin{array}{c}\text { Line } \\ \text { Speed }\end{array} & \begin{array}{c}\text { Number of } \\ \text { Defective } \\ \text { Parts Found }\end{array} \\ 20 & 23 \\ 20 & 21 \\ 30 & 19 \\ 30 & 16 \\ 40 & 15 \\ 40 & 17 \\ 50 & 14 \\ 50 & 11\end{array}$$

a. Develop a scatter diagram with the line speed as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Use the least squares method to develop the estimated regression equation.

d. Predict the number of defective parts found for a line speed of 25 feet per minute.

Volunteers collected non-perishable food items and packaged 14 items per box. If the volunteers collected a total of 200 items, how many boxes could they fill?

Suppose that the distance traveled by a toy car in the first t seconds is $d(t)=20 r^{2}$. What is the velocity of the car at time t?

A rollercoaster at a theme park starts with a vertical drop that leads into two pairs of identical valleys and hills, as shown. a) Write a quadratic function to model the first section of the rollercoaster. b) Write a sinusoidal function to model the second section of the rollercoaster. c) Graph your models and comment on the fit.

In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. At a .05 level of significance, is there a significant difference between the treatments?

$$\begin{matrix} \text{Source} & \text{Sum} & \text{Degrees} & \text{Mean}\\ \text{of Variation} & \text{of Squares} & \text{of Freedom} & \text{Square} & \text{F} & \text{p-value}\\ \text{Treatments} & \text{1200}\\ \text{Error}\\ \text{Total} & \text{1800}\\ \end{matrix}$$

During the 2003 season, Major League Baseball took steps to speed up the play of baseball games in order to maintain fan interest (CNN Headline News, September 30, 2003). The following results come from a sample of 60 games played during the summer of 2002 and a sample of 50 games played during the summer of 2003. The sample mean shows the mean duration of the games included in each sample.

$$\begin{aligned} & 2002 \text { Season } \\ n _ { 1 } = & 60 \\ \overline { x } _ { 1 } = & 2 \text { hours, } 52 \text { minutes } \end{aligned}$$

$$\begin{aligned} & 2003 \text { Season } \\ n _ { 2 } & = 50 \\ \overline { x } _ { 2 } & = 2 \text { hours, } 46 \text { minutes } \end{aligned}$$

A research hypothesis was that the steps taken during the 2003 season would reduce the population mean duration of baseball games. Formulate the null and alternative hypotheses.

In a study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a nonbrowser, light browser, or heavy browser. For each shopper, the study obtained a measure to determine how comfortable the shopper was in a store. Higher scores indicated greater comfort. Suppose the following data were collected.

$$\begin{matrix} \text{ } & \text{Light} & \text{Heavy}\\ \text{Nonbrowser} & \text{Browser} & \text{Browser}\\ \text{4} & \text{5} & \text{5}\\ \text{5} & \text{6} & \text{7}\\ \text{6} & \text{5} & \text{5}\\ \text{3} & \text{4} & \text{7}\\ \text{3} & \text{7} & \text{4}\\ \text{4} & \text{4} & \text{6}\\ \text{5} & \text{6} & \text{5}\\ \text{4} & \text{5} & \text{7}\\ \end{matrix}$$

a. Use $\alpha =$ .05 to test for differences among comfort levels for the three types of browsers. b. Use Fisher’s LSD procedure to compare the comfort levels of nonbrowsers and light browsers. Use $\alpha =$ .05. What is your conclusion?

Four different paints are advertised as having the same drying time. To check the manufacturers' claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded for each sample. The data obtained follow.

$$\begin{array}{cccc}\text { Paint 1 } & \text { Paint 2 } & \text { Paint 3 } & \text { Paint 4 } \\ 128 & 144 & 133 & 150 \\ 137 & 133 & 143 & 142 \\ 135 & 142 & 137 & 135 \\ 124 & 146 & 136 & 140 \\ 141 & 130 & 131 & 153\end{array}$$

Use $\alpha=.05$ to test for any significant differences in mean drying time among the paints.

What is your estimate of mean drying time for paint 2 ? How is it obtained from the computer output?