The nicotine content in cigarettes of a certain brand is normally distributed with a mean µ and a standard deviation σ = 0.1. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but measurements of a random sample of 100 cigarettes of this brand gave a mean xbar = 1.53. Is this evidence at the 5% level of significance that the mean nicotine content is actually higher than advertised?

I have my hypothesis's

H(0): µ=1.5

H(1): µ>1.5

And then I used the TI-83 and entered the following information:

µ(0): 1.5

σ: 0.1

x: 1.53

n: 100

µ: >µ(0)

This gives me the results:

Z-Test

µ>1.5

z=3

p=.0013499672

x=1.53

n=100

And my answer is:

Because .001 is less than the significance level .05, we reject the null hypothesis and instead find sufficient evidence to support the alternative hypothesis.

So it looks like the average amount of nicotine content in cigarettes is higher than advertised.

Is this correct? Because the test statistic was 3, I'm nervous. That just doesn't look right. If you could let me know, I would really appreciate it!!