Q23 of Notes

[Snowy]

Hypothesis testing:
Why is the result of 94% or over very UNlikely at 90% confidence interval?

 

[Margaret Wood]

In Q23, you are testing the null hypothesis that 90% of customers are happy with your service (ie p=0.9) against the alternative hypothesis that more than 90% are happy with your service (ie p>0.9).

In your sample of 100 customers, 94 were happy with your service, ie the sample proportion is 0.94. We want to know if this is significant at the 10% level.

This result will be significant at the 10% level if the probability of getting a sample result as high as this when the true proportion is actually 0.9, is less than 10%. In this case the probability is less than 10%, so the result is significant. It suggests that more than 90% are happy with your service.