please provide solutions for these word problems thank you so much a team of eye surgeons have d

a) We want to test if the new method is different from the old method, so the null hypothesis sh

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A team of eye surgeons have developed a new technique to restore the sight of people blinded from a certain disease. Under the old method it is known that only 31% of patients who undergo this operation recover their eyesight. In a random sample of 299 operations performed using the new method, 100 patients fully recovered their eyesight. a) Select the appropriate null and alternative hypotheses for investigating whether the new method is any different to the old one. π denotes the population proportion that improve under the new method, and p denotes the proportion that improved under the new method within the sample above. 1) H0 : π ≠ 0.31 ; HA : π = 0.31 2) H0 : π = 0.31 ; HA : π ≠ 0.31 3) H0 : μ = 0.31 ; HA : μ ≠ 0.33 4) H0 : p = 0.31 ; HA : p ≠ 0.31 5) H0 : π = 0.33 ; HA : π ≠ 0.33 b) What proportion of patients had their eyesight recovered in the new method in the sample. c) Find the standardized test statistic for this study. d) Calculate the p-value for this test. e) Given the p-value calculated in part d) and α=0.05, select the conclusion which would be appropriate for this hypothesis test. 1) The p-value is greater than or equal to 0.05. There is evidence to reject H0. There is evidence to suggest the percentage who recover their eyesight with the new method is different to the percentage who recover their eyesight under the old method. 2) The p-value is less than 0.05. There is evidence to reject H0. There is evidence that the percentage who recover their eyesight with the new method is different from the percentage who recover their eyesight with the old method. 3) The p-value is less than 0.05. There is insufficient evidence to reject H0. There is not sufficient evidence to conclude that the percentage who recover their eyesight with the new method is significantly different to the percentage who recover their eyesight under the old method. 4) The p-value is greater than or equal to 0.05. There is insufficient evidence to reject H0. There is not sufficient evidence to conclude that the percentage who recover their eyesight with the new method is different to the percentage who recover their eyesight under the old method.

A team of eye surgeons have developed a new technique to restore the sight of people blinded from a certain disease. Under the old method it is known that only 31% of patients who undergo this operation recover their eyesight. In a random sample of 299 operations performed using the new method, 100 patients fully recovered their eyesight.

a) Select the appropriate null and alternative hypotheses for investigating whether the new method is any different to the old one. π denotes the population proportion that improve under the new method, and p denotes the proportion that improved under the new method within the sample above.
1) H0 : π ≠ 0.31 ; HA : π = 0.31
2) H0 : π = 0.31 ; HA : π ≠ 0.31
3) H0 : μ = 0.31 ; HA : μ ≠ 0.33
4) H0 : p = 0.31 ; HA : p ≠ 0.31
5) H0 : π = 0.33 ; HA : π ≠ 0.33

b) What proportion of patients had their eyesight recovered in the new method in the sample.

c) Find the standardized test statistic for this study.

d) Calculate the p-value for this test.

e) Given the p-value calculated in part d) and α=0.05, select the conclusion which would be appropriate for this hypothesis test.
1) The p-value is greater than or equal to 0.05. There is evidence to reject H0. There is evidence to suggest the percentage who recover their eyesight with the new method is different to the percentage who recover their eyesight under the old method.
2) The p-value is less than 0.05. There is evidence to reject H0. There is evidence that the percentage who recover their eyesight with the new method is different from the percentage who recover their eyesight with the old method.
3) The p-value is less than 0.05. There is insufficient evidence to reject H0. There is not sufficient evidence to conclude that the percentage who recover their eyesight with the new method is significantly different to the percentage who recover their eyesight under the old method.
4) The p-value is greater than or equal to 0.05. There is insufficient evidence to reject H0. There is not sufficient evidence to conclude that the percentage who recover their eyesight with the new method is different to the percentage who recover their eyesight under the old method.

Added by Sina L.

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