Question

The average drying time of a wall color is 90 seconds. The research department of the company that produces this type of paint thinks that with the addition of a new chemical component, the drying process of the paint will be accelerated. To verify this assumption, 15 surfaces were covered with paint and the drying time of the paint was measured. where the average time was 86 seconds with a standard deviation of 4.5 seconds. Does this data provide sufficient evidence that the average time for color drying has decreased

Answer 1

Yes, the given data provide sufficient evidence that the average time for color drying has decreased.

Step-by-step explanation:

To determine whether the average time for color drying has decreased with the addition of a new chemical component, we can perform a hypothesis test.

Using a t-test, we compare the sample mean of 86 seconds with the hypothesized population mean of 90 seconds.

The null hypothesis is that there is no change in the average drying time, and the alternative hypothesis is that there is a decrease.

We calculate the test statistic t using the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size)).

With the given data, we find t = (86 - 90) / (4.5 / sqrt(15)) = -2.74.

By comparing the t-value to the critical value at a desired significance level (e.g., α = 0.05), we can determine whether to reject or fail to reject the null hypothesis.

The t-value falls within the rejection region, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the average drying time has decreased.