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My professor's explanation also wasn't very helpful and the question has been bothering me for a couple of days now.

"To show that the mean of burger sold by a particular shop is greater than 2.4 oz, a hypothesis test is carried out under 5% significance level. Given that the variance of the weight is 0.1 oz, find the minimize sample size needed so that the power of the test is at least 0.9 when the true mean of the weight is 2.45 oz."

Would anyone be able to help me figure this out?

I haven't tried any approach because for some reason I'm completely stumped. Might just be looking at the question a bit too many times that I'm confused about what it's really asking me to do.

Randome Nam
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1 Answers1

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power = P(reject H0 | HA is true)

The hypothesis test is H0: mu = 2.4, HA: mu>2.4, alpha=0.05, sigma=0.1, 1-B = power = 0.9, mu = 2.45 (true population mean)

Since sigma is known, this is a Z test. The critical region is (1.645, infinity) (qnorm(.95)) and the test statistic is (Xbar - 2.4)/(0.1/sqrt(n)).

power = P(reject H0 | HA is true)

= P((Xbar - 2.4)/(0.1/sqrt(n)) > 1.645 | mu = 2.45) = 0.9

P(Xbar > 2.4 + 1.645(0.1)/sqrt(n) | mu = 2.45) = 0.9

P(Z > (2.4 + 1.645(0.1)/sqrt(n) - 2.45) / (0.1/sqrt(n))) = 0.9

qnorm(0.1) is -1.282 thus

(2.4+1.645(0.1)/sqrt(n) - 2.45) / (0.1/sqrt(n)) = -1.282

Solve for n to get 34.26932, and round up to require a minimum sample size of 35.

Vons
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