= An experiment compared the durability of two types of exterior house paint; type A was...

 

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= An experiment compared the durability of two types of exterior house paint; type A was an oil-based paint, while type B was latex paint. A total of n₁ = 10 and n = 12 wood panels were covered with paints A and B, respectively. The panels were then exposed to a sequence of tests that involved extreme temperature, light and moisture conditions. At the end of the experiment, the quality of the painted surface was rated on several characteristics (such as paint loss, the lustre of a painted surface, cracking and peeling). Scores between 0 (extremely poor) and 100 (excellent) were assigned to the 22 panels. For paint A, it was found that XA = x and s = 400; for paint B, it was found that g 46 and s3 = 340. Because individual measurements are influenced by numerous random factors, it is reasonable to assume that they are normally distributed. A comparison of s2 = 400 and s3 = 340 shows that the sample variances are quite similar. This provides evidence that the population variances are equal and justifies the pooling of the individual sample variances. Given the 90% confidence interval on the difference between the mean durability of the two paints is (-8.1495, 20.1495), determine the value of x. Next, using a 5% significance level, what can you conclude about the equality of the mean durability of the two paints? Does the 90% confidence interval, (-8.1495, 20.1495) support your conclusion about the equality of the mean durability of the two paints? Please explain your answer. = An experiment compared the durability of two types of exterior house paint; type A was an oil-based paint, while type B was latex paint. A total of n₁ = 10 and n = 12 wood panels were covered with paints A and B, respectively. The panels were then exposed to a sequence of tests that involved extreme temperature, light and moisture conditions. At the end of the experiment, the quality of the painted surface was rated on several characteristics (such as paint loss, the lustre of a painted surface, cracking and peeling). Scores between 0 (extremely poor) and 100 (excellent) were assigned to the 22 panels. For paint A, it was found that XA = x and s = 400; for paint B, it was found that g 46 and s3 = 340. Because individual measurements are influenced by numerous random factors, it is reasonable to assume that they are normally distributed. A comparison of s2 = 400 and s3 = 340 shows that the sample variances are quite similar. This provides evidence that the population variances are equal and justifies the pooling of the individual sample variances. Given the 90% confidence interval on the difference between the mean durability of the two paints is (-8.1495, 20.1495), determine the value of x. Next, using a 5% significance level, what can you conclude about the equality of the mean durability of the two paints? Does the 90% confidence interval, (-8.1495, 20.1495) support your conclusion about the equality of the mean durability of the two paints? Please explain your answer.

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To determine the value of x we need to find the point estimate of the difference between the mean durability of the two paints The point estimate is t... View the full answer