Testing the Pasta Hypothesis: Lasagna Preferences of Pastafarians

[superwolf]

According to a marketing expert, 40% of Pastafarians prefer lasagna. If 9 out of 20 pastafarians choose lasagna over other pastas, what can be concluded about the expert's claim? Use a 0.05 level of significance.

Attempt:

H0: p=0.4
H1: p=/=0.4

Test statistic: Binominal variable X with p=0.4 and n=20.

x=9, and np0 = 8

$$P=1 - \Sigma_{x=0}^9 b(x;20,0.4) = 1 - 0.7553 = 0.2447$$

Correct answer: 0.4044.

??

 

[CompuChip]

You have to add the probabilities for 9, 10, 11, ..., 20. That is the complement (1 - ...) of what?

In other words, you want to calculate the probability that nine or more would prefer the lasagna, which is less than how many?

 

[Mark44]

According to a marketing expert, 40% of Pastafarians prefer lasagna. If 9 out of 20 pastafarians choose lasagna over other pastas, what can be concluded about the expert's claim? Use a 0.05 level of significance.

Attempt:

H0: p=0.4
H1: p=/=0.4

Test statistic: Binominal variable X with p=0.4 and n=20.

x=9, and np0 = 8

$$P=1 - \Sigma_{x=0}^9 b(x;20,0.4) = 1 - 0.7553 = 0.2447$$

Correct answer: 0.4044.

??

You're doing a hypothesis test here, which means that you need a confidence interval. I don't see this anywhere in your work. Since your alternate hypothesis is that p != 0.4, this means you need a two-tailed test, with 0.025 probability in each tail.

The answer you show as correct makes no sense to me in the context of this problem. The answer should be that the expert's claim is accepted or rejected, based on whether the test statistic fell inside our outside of the confidence interval.