I really need help in these statistic questions?

Question

1- a hypothetis test has a decision of "reject the null hypothesis". what type of error might be made on this problem?
2- a 95% confidence interval for a population mean goes from 188 to 268, what was the mean of the sample?
3- if u fail to reject the null hypothesis, what type of error u might be making?
4- which one can be a p value and why: ( -0.054, 3.2 E-5, -1.35, 1.87 ) ?
thnak you so much in advance

Answer 1

1. both type I and II errors

2. average of 188 and 268 i.e. 228

3. type II

4. 3.2e-5 because p has to be between 0 and 1

Answer 2

1. Sorry, Cherry, but you have things the wrong way around. If you reject the null hypothesis, the error you may be making is if the null hypothesis is in fact true.



In a Type I error, the null hypothesis is true, but is (falsly) rejected. So the danger here is of making a Type I error.





2. A 95% confidence interval is an interval of ±1.96 standard deviations about the mean. So the confidence interval is centred on the mean value. The length of the confidence interval is 80, so the mean is at the 40 point, that is, 188 + 40 = 228.



3. A Type II error occurs when the null hypothesis is really false, but the evidence is not strong enough to reject it. So if you wrongly accept the null hypothesis, you are making a Type II error, which is the danger here.



It can be difficult to remember which is which. It might help to remember just this :



Type I error -- the null hypothesis is true



Type II error -- the alternative hypothesis is true



(it is then self-evident that if you make the error, in Type I you reject, and in Type II you accept, the null hypothesis).



4. I am not very familiar with the use of p-values, but as I understand it, the p-value is the lowest significance level at which the null hypothesis is rejected. It is a probability, in other words, so it should be a positive number less than 1, which would rule out -0.054, -1.35 and 1.87 as p-values. That leaves only 3.2 E-5, which seems so extraordinarily low that you would never reject the null hypothesis. So all these values look to be unlikely p-values. Usually, I think a reasonable p-value would be round about the 0.01 to 0.1 range, which makes the 0.054 value seem about right, except that it has that minus sign. So I think that you will have to decide this one for yourself.

Answer 3

1. When you reject the null hypothesis, you have a chance of making a "Type I Error", where you are rejecting H-naught when it is in fact true. This probability is denoted by alpha.



2. I'm not sure about this one. If you have a 95% confidence interval, this means that if you repeatedly sample your population, your mean will be in [188, 268] 95% of the time.



3. If you fail to reject the null hypothesis, you have a chance of making a "Type II Error" where you accept H-naught when your alternative is in fact true. This is probability is called beta in my class.



4. The p-value is the probability that your true parameter/test statistic/etc. will be greater than the value you obtained from your sample, while assuming your null hypothesis is true. So, I'm not sure which of those values applies to your question.



I'd assume it would be the one in [0,1], since it is a probability.



Hope this helps some.

Answer 4

1 - Type II Error - the null hypothesis appeared to be true, but the alternative hypothesis ended up to be true.



2 - ?



3 - Type I Error - sampling error - the belief that the null hypothesis was wrong and that the alternative hypothesis was right is proved to be false



4 - ?

Answer 5

idk