A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trou

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2 months ago

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A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trou

gh that is made out of a 14-gauge steel coil. It is produced using a 250-ton progressive punch press with a wipedown operation that puts two 90-degree forms in the flat steel to make the trough. The distance from one side of the form to the other is critical because of weatherproofing in outdoor applications. The company requires that the width of the trough be between 8.31 inches and 8.61 inches. The widths of the troughs, in inches, collected from a sample of 49 troughs are:
8.312, 8.343, 8.317, 8.383, 8.348, 8.410, 8.351, 8.373, 8.481, 8.422, 8.476, 8.382, 8.484, 8.403, 8.414, 8.419, 8.385, 8.465, 8.498, 8.447, 8.436, 8.413, 8.489, 8.414, 8.481, 8.415, 8.479, 8.429, 8.458, 8.462, 8.460, 8.444, 8.429, 8.460, 8.412, 8.420, 8.410, 8.405, 8.323, 8.420, 8.396, 8.447, 8.405, 8.439, 8.411, 8.427, 8.420, 8.498, 8.409
a. Construct a frequency distribution and a percentage distribution.
b. Construct a cumulative percentage distribution.
c. What can you conclude about the number of troughs that will meet the company's requirements of troughs being between 8.31 and 8.61 inches wide?

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-02-17T13:38:25+03:00

Answer:

Please refer to the explanation.

Step-by-step explanation:

(a)

H0: The mean of the population = 8.46

H1: The population mean differs from 8.46

The following equation represents the test statistic (t):

${t=\frac{\overline{x}-\mu_0}{s/\sqrt{n}}}$

We have determined the sample mean (8.421) and the sample standard deviation (0.0461). Consequently, the test statistic (t) is calculated as follows:

t = (8.421 - 8.46)/(0.0461/sqrt(49)) = -5.92

The left-tailed critical value from the t-distribution (two-tailed) is -2.01. Thus, the test statistic falls within the rejection zone, leading us to reject the null hypothesis at a 95% confidence level, indicating that the population mean is different from 8.46 inches.

(b)

The four assumptions for a single sample t-test are as follows:

The data collected must be on a ratio scale.

All observations need to be independent and not correlated.

No significant outliers should be present within the sample data.

The sample data should have a normal distribution.

(c)

The first assumption holds true since the data is measured in inches. The second assumption cannot be directly tested now; it relies on the context and study design which we assume to be valid in this instance. The presence of outliers can be evaluated by creating a box plot. The final assumption can be verified through the Anderson-Darling normality test.

Please review the graphical representation in the images provided below.

(d)

The data appears to follow a normal distribution (with a p-value from the Anderson-Darling test exceeding 0.05). There are two outliers identified in the box plot, although they do not differ drastically from the rest of the dataset. Therefore, we determine that the assumptions are satisfied for conducting the t-test.