Significance testing in 5 different situations
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1. Suppose you want to test the claim that the population mean(u) is < or equal to 25.6. Given a sample size of n=44 and a level of significance of 0.05, when should you reject the null hypothesis?
2. Given the null hypothesis: population mean = 25 and the alternative hypothesis population mean not equal to 25, and P=0.041. Do you reject or fail to reject the null hypothesis at the 0.01 level of significance?
3. It is desired to test the null hypothesis: population mean (u) =40 against the alternative hypothesis: population mean (u) < 40 using the level of significance = 0.10. The population in question is uniformly distributed with a standard deviation of 10. A random sample of 36 will be drawn from this population. If the population mean (u) is really equal to 35, what is the probability that the hypothesis test would lead the investigation to commit a Type II error?
4. Find the critical value for a two-tailed test with the level of significance (a) = 0.08.
5. The mean age of bus driver in Chicago is 45.6 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
The mean age of bus drivers in Chicago is 53.2 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?
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Solution Summary
This solution solves 5 difference hypothesis testing problems. These cover different significance levels and test statistics.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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- "Thank you very much for your valuable time and assistance!"
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