Answer :
The p-value for the test is 0.001.
To determine the p-value for the test, we need to perform a hypothesis test to assess if the modification in the manufacturing process has increased the mean acceptable transmission distance.
The null hypothesis (H0) assumes that there is no significant increase in the mean acceptable transmission distance. The alternative hypothesis (H1) suggests that there is a significant increase in the mean acceptable transmission distance.
We can conduct a one-sample t-test to compare the sample mean to the hypothesized population mean. In this case, the hypothesized mean is 58 km.
The test statistic can be calculated using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Substituting the given values, we have:
t = (59.1 - 58) / (2.31 / sqrt(40))
Calculating the value of t, we find:
t ≈ 6.52
Next, we need to determine the p-value associated with this test statistic. The p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.
Since the sample size is relatively large (n = 40) and we assume a normal distribution, we can use the t-distribution to find the p-value. In this case, we are performing a one-tailed test (since we are interested in whether the mean has increased), so we look up the p-value corresponding to the observed t-value in the upper tail of the t-distribution.
Looking up the p-value associated with t ≈ 6.52 in the upper tail of the t-distribution, we find that it is approximately 0.001.
Therefore, the p-value for the test is 0.001, indicating strong evidence against the null hypothesis. This suggests that the modification in the manufacturing process has led to a significant increase in the mean acceptable transmission distance.
Learn more about null hypothesis here:
brainly.com/question/30821298
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