Help on T Distribution and Skewness Questions

[sosme]

I am a bit unsure on three question can anybody help me out? My attempts are marked with *

Find P(Mu > xbar); where xbar = -96.52, Mu0 = -34.21, n = 15, s2 = 32193.0551
**I wanted to use the t-distrbtion formula but I am not sure about Mu0, do I assume that Mu0=Mu and for s do I just plug it into this formula http://www.psych.utoronto.ca/courses...7/chapte17.gif
but the thing is I see in my book s, sigmaxbar, sigma -> what's the difference between these, they seem like all the same


Calculate xbar where P(Mu > xbar) = 0.025, df = 20, Muxbar = 39.4, sigmaxbar = 28.7

*I tried to use the t-distriubution formula but I am still confused about the difference between xbar, Mu0, muxbar and Mu they seem like the same :S espiecally muxbar (is that the SD of the mean sample but then isn't that xbar :S Can I just plug sigmaxbar into S in the formula t = (xbar - mu)/(s/sqrt n) :S:S


In a similar test that was powered at 95%, you examined whether the use of advil among women attending your store was different from the general population. You conducted the test with 98% confidence, and found that the use of advil at your store was higher, but similar to and not significantly different than the general population. What was the probability that you were wrong?

Choices
a. 0.050
b. 0.020
c. 0.200
d. None of the other answers

*I thought that it was 0.02 at first but then I started thinking about the 95%, what does that mean? What about alpha error?


Your friend is saying that you should not be using a Z or T test to test your hypothesis because the distribution of advil use in the general population of women is highly skewed. What do you say?
1) we will redo the tests in a way that does not rely on normality
2) It is fine because the Central Limit Theorem states that Sigmaxbar = Sigma0 / sqrt (N)

***I narrowed it down to these two but I can't figure out whether it's 1 or 2. How do I reason this out? I know that with CLT that statement is right but does that mean it's correct for this question?


thank you so so much

 

[Valkarie]

for trying to help me out :D[A] For the first question, you need to use the t-distribution formula. Mu0 is the population mean, s is the standard deviation of the population, and xbar is the sample mean. The formula is t = (xbar - mu0) / (s/sqrt n). Plug in the given values and solve for P(Mu > xbar). To calculate xbar, you need to use the inverse t-distribution formula. The formula is xbar = mu0 + (s/sqrt n) * t. Plug in the given values and solve for xbar. [C] For this question, you should choose option 1. The Central Limit Theorem states that the sample mean will be approximately normally distributed even when the population is highly skewed. However, it is best to redo the tests in a way that does not rely on normality to ensure the most accurate results.