null hyppthesis  TOPIC_SOLVED

Standard deviation, mean, variance, z-scores, t-tests, etc.

null hyppthesis

Postby yabo2k on Mon Oct 26, 2009 9:50 pm

Consider the following hypothesis test
Ho: >= 20
Ha: < 20
A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

a- compute the value of the test statistic? I got 2.12
b- what is the p-value? is it .017 or is it .9830 because it is upper tail
c- using alpha=.05, what is your conclusion?
d- what is the rejection rule using critical value?
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Re: null hyppthesis  TOPIC_SOLVED

Postby ilearnmath.net on Fri Nov 27, 2009 1:25 am

Hi:
The t-statistic should be negative, since your sample mean is less than the hypothesized value of 20.

A T-test on the TI-84 gives:

t=-2.1213
P-value = 0.019489

The P-value measures the probability of observing a sample mean as extreme or more extreme than the one that has been observed. Because the P-value is less than the significance level of 0.05, we reject the null in favor of the alternative hypothesis.

The rule is:
If P is less than alpha, reject the null hypothesis.
If P is greater than alpha, fail to reject the null hypothesis.

I hope this helps.

Good luck!
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