1) State the null and alternative hypotheses for the following two studies. (20 marks)

(i)The mean entry level salary of an employee at a company is $58,000. You believe it is higher for IT professionals in the company.(6 marks)

(ii)A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is correct.(6 marks)

(iii)You flip a coin and record whether it shows heads or tails. You know the probability of getting heads is 50%, but you think it is less for this particular coin. State the null and alternative hypotheses. What type of test would you use?(8marks)

2) The cost of a daily newspaper varies from city to city. It was assumed that the daily newspaper cost follows a normal distribution with a standard deviation of 30. A study was done to test the claim that the mean cost of a daily newspaper was $1.00. A sample of 36 costs yield a mean cost of $1.05. Do the data support the claim at the 1% significance level?(20 marks)

3) A small component in an electronic device has two small holes. In the manufacturing process, the average distance between the two holes must be tightly controlled at0.02mm, else many units would be defective and wasted. Many times throughout the day, quality control engineers take a smallsampleof the components from the production line, measure the distance between the two holes, and make adjustments in the manufacturing process if the average distance is more than 0.02 mm.

Suppose at one time, four units are randomly taken and the distances are measured (in mm) as 0.021, 0.019, 0.023, 0.020. The sample meanand standard deviationsare found to be 0.02075 mm and 0.00171 mm respectively.

Determine, at the 5% level of significance, if there is sufficient evidence in the sample to conclude that an adjustment in the manufacturing process is needed. Assume the distances of interest are normally distributed.(20 marks)

Show your working details including all the steps of a hypothesis test. Computation of the test statistic should be done at 5 decimal places.