# Hypothesis testing

1. Oct 15, 2013

### BCCB

In a sample of 100 people. 50 people like ice cream, of those 50 people, 25 like chocolate.

Calculate with 95% confidence, that over 60% of people like his chocolate ice cream.

H_0= mu > 0.60
H_1=mu < 0.60

25/50=0.50% of people like chocolate ice cream

(0.50-0.60)/ [100(0.60)(0.40)]^(1/2)= -0.1/24= - 0.00417

z crit = 1.96 therefore, we can not reject the null

is this right?

Thanks

2. Oct 15, 2013

### Staff: Mentor

In the numerator, you use percentages, in the denominator, you use people. Those do not match.

60% of all? Then you have just 25 of 100. 60% of those that like ice cream? Then your sample size is just 50.

In both cases, you still have to assume that "likes ice cream" and "likes chocolate" implies "likes chocolate ice cream".
The wording looks really strange in general.

3. Oct 15, 2013

### BCCB

I'm assuming it is 60% of the total population. so if that's the case your saying that I should use 25/100 rather than the 25/50? then I don't know what the sample of 50 subset of people is for ( I don't know why that is included in the question).

I don't know what to do

4. Oct 15, 2013

### Staff: Mentor

Is this the exact problem statement?

5. Oct 15, 2013

### BCCB

An ice cream owner randomly samples 100 people. He finds that 50 people like ice cream and of those 50 people, 25 like chocolate ice cream. Calculate with 95% confidence that over 60% of people like his chocolate ice cream.

It just occurred to me that it was not clear that the 50 people liked chocolate ice cream not just chocolate! Sorry about that.

6. Oct 15, 2013

### Staff: Mentor

I think that part is clear:

100 sampled:
50 of them do not like ice cream
25 of them do like ice cream, but not chocolate ice cream
25 of them do like ice cream, including chocolate ice cream

Okay, strange problem statement. And the observed 25% are far way from 60%.

7. Oct 16, 2013

Calculate with 95% confidence means you want a confidence interval, not a hypothesis test.

8. Oct 16, 2013

### Staff: Mentor

Confidence interval for the measurement? Where is the point in the 60% then?
Confidence interval for the 60%? Where is the point in the data sample then?

9. Oct 17, 2013

### kurros

Possibly the question is really wanting a p-value for the hypothesis than 60% or more of the population like chocolate ice cream. Though that would require a prior on the fraction of people who like chocolate ice cream. Hmm. Maybe just then the p-value for 60% of the population liking chocolate ice-cream? Anyway the problem is very badly stated.