if Ho:Mu=50 and Ha:mu 59 and beta=10 what is alpha if x exceeds 56 for n=49
To determine the value of alpha given the hypotheses and the information about beta and sample size, we need to understand the concepts of alpha, beta, and significance level.
In statistical hypothesis testing, alpha (α) represents the significance level, which is the probability of rejecting the null hypothesis (Ho) when it is actually true. It denotes the risk of committing a Type I error, which is rejecting a true null hypothesis.
On the other hand, beta (β) represents the probability of accepting the null hypothesis (Ho) when the alternative hypothesis (Ha) is true. It denotes the risk of committing a Type II error, which is failing to reject a false null hypothesis.
Given:
- Null hypothesis (Ho): μ = 50
- Alternative hypothesis (Ha): μ > 59 (one-sided alternative)
- Beta (β): 10 (β = 0.10)
- Sample size (n): 49
- x exceeds 56
To find alpha (α), we first need to calculate the critical value of the test statistic for a given significance level (alpha). The critical value is compared to the observed test statistic (sample statistic) to decide whether to reject the null hypothesis or not.
However, in this case, we are given beta and need to determine alpha. We can calculate alpha using the following equation:
alpha = 1 - beta
Given beta = 0.10, we can substitute it into the equation to find alpha:
alpha = 1 - 0.10
alpha = 0.90
Therefore, the value of alpha is 0.90 (or 90%). This means that if the observed test statistic exceeds the critical value corresponding to alpha = 0.90, we would reject the null hypothesis at a 90% level of significance.