Hypothesis testing (MR, unit 10)

the process of establishing the significance of the results of sample data for hypotheses about the population

1. Establish a hypothesis. H0 a null hypothesis (mean value is £200) H1 an alternative hypothesis (mean value is not £200)
2. Select a significance level, which indicates how severely we're testing the null hypothesis
3. Calculate the standard error and the distance from the mean in standard deviations
4. Test the hypothesis.

John thinks people won't pay more than £40 for this new product
Mean sample of 150 said they'd pay £45 with a standard deviation of £10
We'll use significance level of 5% (this is commonly used)

So we need to find out that the sample mean is within a 95% confidence interval around the null hypothesis
SE = o/]n
SE = 10/]150
SE = 0.816

At 5% level of confidence, we expect the mean to be within 1.96 standard errors of the hypothesised mean
It is 6.1 SE above the mean (5/0.816)

Conclusion: John's wrong! If it had have been within 1.96 SEs, it wouldn't mean he's right, just that we don't have enough evidence to reject the null hypothesis.