I need help with this question.

5. Before we sign a contract to purchase the apples produced by King's Apple Orchard,

we want to study the proportion of apples produced there with insect bites.

(a) (11 points) To construct a 90% confidence interval for the proportion of apples

with insect bites, we need to survey a random sample of apples. If the margin of

error must be kept within 3%, what should be the minimum size of the sample we

should survey?

(b) (13 points) We actually surveyed a random sample of 1000 apples. Among these

apples, 43 with insect bites. Construct a 90% confidence interval for the proportion

of all apples there with insect bites.

Confidence interval:

margin of error:

Interpretation:

Which of the calculator procedures have you used?

ZInterval TInterval 1-PropZInt

(c) (22 points) An agricultural expert claims that the proportion of apples with insect

bite from King's Apple Orchard is 5%. We believe that the claim is not accurate. Is

the sample evidence from (b) strong enough, at 0.1 level of significance to reject

the agricultural expert's claim?

h0: ha:

Alpha=?

Find critical value, rejection region, and the standardized test statistic OR p-

value of the test.

Conclusion:

Interpretation: At 10% level of significance the agricultural expert's claim that

the proportion of insect bite apples from King's Apple Orchard is 5% should

be rejected; not be rejected; be supported; not be supported

Which of the calculator procedures you have used?

Z-Test T-Test 1-PropZTest