The department of transportation has mandated that the average speed of cars on interstate
highways be no more than 70 km per hours in order. To check that the people follow it or not,
a researcher took a random sample of 186 cars and found that the average speed was 72 km
per hours with a standard deviation 0.6 km per hours.
(a) Construct the interval around the sample mean that would contain the population mean 95% of the time.
(b) If the researcher wants to test that the true mean speed on its highways is 70 km per hours or less with 95% confidence then
(i) State null and alternative hypotheses.
(ii) Name the test which is suitable in this situation and why?
(iii) Calculate the value of test statistic and critical value.
(iv)Draw the conclusion on the basis of the applied test

To solve this problem, we need to perform a hypothesis test to determine whether the true mean speed on the interstate highways is 70 km/hour or less.

Given:
- Sample size (n) = 186
- Sample mean (x̄) = 72 km/hour
- Sample standard deviation (s) = 0.6 km/hour
- Desired confidence level = 95%

(a) Construct the interval around the sample mean that would contain the population mean 95% of the time.

The 95% confidence interval for the population mean (μ) is given by:

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