# Thread: standard deviation and hypothesis testing

1. ## standard deviation and hypothesis testing

Hi guys.

Im new at this site so please be nice to me =P. Ive been working on some practice papers for my upcoming end of semester exams. Cant get these two questions out ><. Any help is greatly appreciated

jenny xoxo

1. A sample of 28 students measured their reaction time by recording the distance a dropped ruler fell before they caught it. This was then repeated to see whether a learning effect was present. The mean decrease in drop distance between the two trials was 1.69 cm with standard deviation 1.916 cm. The margin of error for a 95% confidence interval for the mean decrease in drop distance for all students is ____

2. Suppose we are taking samples from a population that has the same numbers of males and females but are concerned the sampling method may be biased. We take a sample of 20 people and test the null hypothesis H0: p = 0.5, where p is the mean proportion of females in a sample produced by the method.
The power of this test to detect a bias at the 5% level if the sampling method actually produces at least 70% females is ____

2. Hi Jenny,

Here is some help for you.

1. This one is only an application of the formula for confidence intervals: the margin of error is given by $\displaystyle \frac{\sigma\Phi_{0.95}}{\sqrt{n}}$, where $\displaystyle \Phi_{0.95}$ is such that $\displaystyle P(|N|<\Phi_{0.95})=0.95$ for a standard normal random variable $\displaystyle N$, i.e. $\displaystyle \Phi_{0.95}\simeq 1.96$ (you may be used to another notation for this quantity). Just replace $\displaystyle n$ and $\displaystyle \sigma$ by their values in the formula and take your calculator.

2. Here are steps: First find the test the question is about. This amounts to finding a 95% confidence interval for the proportion of females among 20 people, males and females being equally likely. Then look for the probability that the proportion of females falls outside this interval (i.e. the test tells "H0 is false"), in the case when the probability of a female is no more 0.5 but 0.7 (you can approximate the proportion of women by a normal random variable of mean 0.7 and stdd deviation $\displaystyle \frac{\sqrt{0.7\cdot(1-0.7)}}{\sqrt{20}}$). This reduces to looking up in tables quantities like $\displaystyle P(N<0.14)$ where $\displaystyle N$ is a standard Gaussian random variable. I leave it to you to precise all this...

I hope this helped you,
Laurent.

3. for 1. i still cant get the answer. my n=23, mean=1.65 and sd=2.14 at 95% confidence.