Testing H0: μ=0 Against Ha: μ≠0 with 10 Observations

[melissa5789]

Homework Statement

For a quantitative variable, you want to test H0; $$\mu$$=0, against Ha, mu not equal 0. The 10 observations are 3,7,3,3,0,8,1,12,5,8

a. I get this part
b. The P-value is 0.002. Interpret, and make a decision using a significance level of 0.05. Interpret.
c. If you had used Ha: mu>0, what would the P-value be? Intrepret.
d. If you had instead used Ha: mu<0, what wold the P-value be? Intrepret it.

Homework Equations

b.
Does intrepret mean draw it, or say it? I have the table, but the value don't go as low as 0.002. What do I do?

c&d. I'll probably understand this if I can understant part b.
Help me please. xoxoxoxox

The Attempt at a Solution

 

[Tedjn]

You can draw a normal curve, and indicate what p = 0.002 for a two-sided test means on there, but you should also explain it in words. What does a probability of 0.002 mean; in other words, what has a 0.002 chance of occurring? When you perform your test, what are you assuming is true?

 

[Architeuthis Dux]

a. I understand that you are testing a null hypothesis (H0) that the population mean (μ) is equal to 0 against an alternative hypothesis (Ha) that the population mean is not equal to 0. You have 10 observations for a quantitative variable, which are 3, 7, 3, 3, 0, 8, 1, 12, 5, 8.

b. The P-value is the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true. In this case, the P-value is 0.002, which means that there is a 0.2% chance of obtaining a sample mean as extreme as the one observed if the population mean is actually 0. Since this probability is lower than the significance level of 0.05, we reject the null hypothesis and conclude that there is enough evidence to suggest that the population mean is not equal to 0.

c. If the alternative hypothesis was Ha: μ>0, the P-value would be the probability of obtaining a sample mean as extreme as the one observed or even more extreme, assuming the null hypothesis is true. This would be a one-tailed test, so the P-value would be half of the P-value in part b, which is 0.001. This means that there is a 0.1% chance of obtaining a sample mean as extreme as the one observed or even more extreme if the population mean is actually 0. Again, this probability is lower than the significance level of 0.05, so we would still reject the null hypothesis and conclude that the population mean is greater than 0.

d. If the alternative hypothesis was Ha: μ<0, the P-value would be the probability of obtaining a sample mean as extreme as the one observed or even more extreme in the opposite direction, assuming the null hypothesis is true. This would also be a one-tailed test, so the P-value would still be 0.001. However, in this case, the extreme value would be in the negative direction, so the P-value would be interpreted as the probability of obtaining a sample mean as extreme as the one observed or even more extreme in the negative direction. This means that there is a 0.1% chance of obtaining a sample mean as extreme as the one observed or even more extreme in the negative direction if the population mean is actually