Question

A)An article reports that in a sample of 113 people undergoing a certain type of hip replacement surgery on one hip, 64 of them had surgery on their right hip. Can you conclude that frequency of this type of surgery differs between right and left hips? Find the P-value and state a conclusion. Round the answer to four decimal places. The P-value is?

B)Lasers can provide highly accurate measurements of small movements. To determine the accuracy of such a laser, it was used to take 95 measurements of a known quantity. The sample mean error was 22 ?m with a standard deviation of 65 ?m. The laser is properly calibrated if the mean error is ? = 0. A test is made of H₀ : ? = 0 versus H₁ : ? ? 0.

- Find the P-value. Round the answer to four decimal places.

-The P-value calculated for testing H₀ : µ = 0 versus H₁ : µ ? 0 is a very small probability; hence, it is plausible that the laser is out of calibration. TRUE OR FALSE .

C)A machine that fills cereal boxes is supposed to be calibrated so that the mean fill weight is 12 oz. Let ? denote the true mean fill weight. Assume that in a test of the hypotheses H₀ : ? = 12 versus H₁ : ? ? 12, the P-value is 0.31.

-Should H₀ be rejected on the basis of this test? Explain. Check all that are true?

-Can you conclude that the machine is calibrated to provide a mean fill weight of 12 oz? Explain. Check all that are true?

D) An article reports that in a sample of 113 people undergoing a certain type of hip replacement surgery on one hip, 64 of them had surgery on their right hip. Can you conclude that frequency of this type of surgery differs between right and left hips? Find the P-value and state a conclusion. Round the answer to four decimal places. The P-value is?

Answer 1

(A) p-value=0.158

here null hypothesis H0:P=0.5 and alternate hypothesis H1:P is not =0.5

p=x/n=64/113=0.5664

test statistic z=(p-P)/SE(p)=(0.5664-0.5)/sqrt(0.5*(1-0.5)/113)=1.4117

p-value=P(|Z|>1.4117)=2*P(Z>1.4117)=2*(1-P(Z<1.4117)=2*(1-0.9210)=0.1580

(B) answer is FALSE

p-value=0.001

test statistic z=(x^--mu)/(s_d/sqrt(n))=(22-0)/(65/sqrt(95))=3.2989

p-value=P(|Z|>3.2989)=2*P(Z>3.2989)=2*(1-P(Z<3.2989)=2*(1-0.9995)=0.0010

since p-value is less than typical alpha=0.05, we reject the null hypothesis and conclude that there is need of calibaration of laser machine

(C) we should not reject the null hypothesis as the p-value is more than typical alpha=0.05

(D) same as part A.