1) A null Hypothesis assumes that a process is producing no more than a maximum allowable rate of defective items. The Type II error is to conclude that the process?
2) If 95% confidence limits for the mean Mu turn out to be (6.5,8.5)
bruh this was the first everq uestion on jishka , posteddd on june something 2005
From Google:
Type II error is failing to reject a false null hypothesis (also known as a "false negative" finding).
Confused by "(6.5,8.5)." If 8.5 = standard deviation, over 16% will be in the negative area.
lol @frankly frank your right , i just looked on that thread
lol same. I just posted there XD
1) The Type II error is when we incorrectly fail to reject the null hypothesis, even though it is false. In the context you mentioned, it means we conclude that the process is producing no more than the maximum allowable rate of defective items, even though it is actually producing more.
To determine the Type II error, we need to conduct a hypothesis test. The null hypothesis assumes that the process is producing no more than the maximum allowable rate of defective items, while the alternative hypothesis assumes that the process is producing more defective items. We collect data and calculate a test statistic, and then compare it to a critical value or p-value to make a decision.
If the test statistic does not exceed the critical value or if the p-value is greater than our chosen significance level, we fail to reject the null hypothesis. However, if the test statistic exceeds the critical value or if the p-value is less than the significance level, we reject the null hypothesis in favor of the alternative hypothesis.
Therefore, the Type II error occurs when we fail to reject the null hypothesis (concluding that the process is producing no more than the maximum allowable rate of defective items), even though it is actually producing more defective items.
2) If the 95% confidence limits for the mean Mu are (6.5, 8.5), it means that we are 95% confident that the true population mean falls within this range.
To obtain these confidence limits, we need to perform a confidence interval calculation using sample data. We typically use a t-distribution or z-distribution, depending on the sample size and whether we know the population standard deviation.
The general formula for constructing a confidence interval for the population mean is:
Confidence interval = sample mean ± margin of error
The margin of error depends on the desired confidence level and the standard deviation of the population (or the sample, if it is representative). For a 95% confidence level, we use a significance level of alpha = 0.05.
Assuming a normal distribution and a known population standard deviation, the margin of error is calculated as:
Margin of error = (critical value) * (standard deviation / √sample size)
Here, the critical value is determined by the distribution and the desired confidence level. For a large sample (typically considered as n ≥ 30), we use a z-distribution and the critical value is obtained from the standard normal distribution table. For smaller sample sizes, we may use a t-distribution instead.
Once we calculate the margin of error, we can construct the confidence interval by adding and subtracting it from the sample mean. In this case, the confidence interval would be (6.5, 8.5), indicating that we are 95% confident that the true population mean falls within this range.