I need help with this question

We are commissioned to study the traffic flow on a section of a Banana Republic

highway. The standard deviation of all speeds of cars passing through that section can

be assumed 8.3 mph.

(a) (11 points) To construct a 95% confidence interval for the mean speed of all cars

we need to measure a random sample. If the margin of error of the estimation must

be kept within E = 2 mph, what should be the minimum size of the sample we

should measure?

(b) (13 points) We actually recorded the speeds of n = 80 randomly selected cars on

that section and found that the sample mean speed 66.9 mph. Construct a 95%

confidence interval for the mean speed of all cars on that section, find the margin of

error of the estimation, and interpret the result in English.

Confidence interval:

Margin of error:

Interpretation:

Which of the calculator procedures have you used?

ZInterval TInterval 1-PropZInt

(c) (22 points) Use the information from (b) to test, at 0.05 level of significance,

whether the sample evidence is strong enough to support the claim that the mean

speed of all cars on that section is faster than the posted speed limit of 65 mph.

Complete the following steps.

h0: ha:

alpha= ?

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

value of the test.

conclusion:

Interpretation: At 5% level of significance the claim that the mean speed of all

cars on that section is faster than 65 mph 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