You are trying to decide if a coin is fair What should your

You are trying to decide if a coin is fair What should your null and alternative hypotheses be? Should you use a two-sided or a one-sided test? In the context of this problem [e.g. flipping coins], give an example of a Type I error, and an example of a Type II error If you want to test your null hypothesis by flipping the coin 10,000 times, what would the rejection region be, roughly, if alpha = 0.05? The average US life expectancy is about 78 years. You are trying to decide if the average life expectancy among Californians is different from that of the entire US What should your null and alternative hypotheses be? Should you use a two-sided or a one-sided test? You read the records of 400 randomly chosen deceased Californians, and you find that their average age at death is 76 years, with a population standard deviation of 15 years. Write down the exact p-value of this data. You can leave your answer as an integral Can you reject the null hypothesis for alpha = 0.05, given your answer to (b)? You may use a calculator or the normal distribution or t-distribution applets at: http://www.stat.berkeley.edu/stark/Java/Html/NormHiLite.htm http://www.stat.berkeley.edu/stark/Java/Html/tHiLite.htm if you need help estimating the integral Repeat all parts of the previous problem, but this time you are deciding if the average life expectancy among Californians is less than that of the entire US, and you only pick 4 deceased: you find that their ages at death were 65 years, 74 years, 80 years, and 85 years.

Solution

1: null hypothesis is that the coin is not fair against alternative hypothesis is that the coin is fair. 2: Ho:there is no a significant difference between the averages life expectancy among californians versus the entire US. Against H1: there is a significant difference between the averages life expectancy among californians versus the entire US. Here n=400 ,so given sample is large ,so we use Z test. Xbar=76, =15,=78, Zcal=|xbar-|/(/n)=(76-78)/(15/400)=2.667, Z table value for two-tailed test is 1.96, here Zcal>Ztab, so we reject null hypothesis. Therefore, there is a significant difference between the averages life expectancy among californians versus the entire US. 3:Ho:it is concluded that the averages life expectancy among californians is less than that of the entire US. Against H1:it is not concluded that the averages life expectancy among californians is less than that of the entire US. Here n=400 ,so given sample is large ,so we use Z test. Xbar=76, =15,=78, Zcal=(xbar-)/(/n)=(76-78)/(15/400)=-2.667, Z table value for left-tailed test is -1.645,here Zcal<Ztab, so we accept null hypothesis. Therefore, it is concluded that the averages life expectancy among californians is less than that of the entire US.