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)
A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null hypothesis that is actually false. The error rejects the alternative hypothesis, even though it does not occur due to chance.
Complete #2.
Congrats @Frank, after nearly 14 years you finally got part of your answer!
1) The Type II error in this case would be to conclude that the process is producing more than the maximum allowable rate of defective items when in reality it is not.
2) The 95% confidence limits for the mean Mu are (6.5, 8.5). This means that we can be 95% confident that the true population mean falls within this range.
1) In hypothesis testing, the null hypothesis (H0) assumes that a process is producing no more than a maximum allowable rate of defective items. The null hypothesis typically represents the status quo or no effect scenario. On the other hand, the alternative hypothesis (Ha) assumes that there is a difference or an effect in the process.
A Type II error occurs when we fail to reject the null hypothesis (H0) when it is actually false (i.e., we conclude that the process is not producing more defective items when it actually is). In other words, a Type II error is a false negative, where we miss detecting a true effect or difference in the process.
To avoid making Type II errors, it is essential to conduct hypothesis testing with a sufficient sample size and statistical power. Statistical power refers to the probability of correctly rejecting the null hypothesis when it is false. By increasing the sample size or designing experiments with higher power, we can reduce the chances of making a Type II error.
2) The 95% confidence limits for the mean (μ) turning out to be (6.5, 8.5) means that we are 95% confident that the true population mean falls within this interval. This confidence interval is constructed based on a sample mean and the associated standard error.
To calculate the confidence interval, we typically use the t-distribution for small sample sizes or the normal distribution for large sample sizes. The formula is:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Error)
Where:
- Sample Mean: The mean obtained from the sample data
- Critical Value: The value obtained from the t-distribution or z-distribution based on the desired level of confidence (in this case, 95% confidence)
- Standard Error: The standard deviation of the sample mean, calculated by dividing the sample standard deviation by the square root of the sample size.
By calculating the values of the sample mean, critical value, and standard error, we can construct a confidence interval that gives us a range of values within which we are 95% confident that the true population mean lies. In this case, the interval is (6.5, 8.5), indicating that the true mean is expected to fall between 6.5 and 8.5 with 95% confidence.