DIRECTIONS: Answer P1-4 SHOW YOUR SOLUTIONS.

PROBLEM 1 (10 points)

A printer manufacturing company claims that its new ink-efficient printer can print an average of 1500 pges of words documents with a standard deviation of 60. Forty-nine (49) of these printers showed a mean of 1475 pges. Does this support the company's claim? Use 0.05 level of significance.

PROBLEM 2 (10 points)

The average lifetime of 150 Samsung batteries and 150 Huawei batteries were found to be 10.1 hours and 10.6 hours respectively. Suppose the population standard deviations of lifetimes are 2.9 hours for Samsung while 3.1 hours for Huawei. Test the hypothesis using 0.1 level of significance.

PROBLEM 3 (10 points)

The treasurer of a certain university claims that the mean monthly salary of their college professor is 21,750 pesos with a standard deviation of 6,000 pesos. A researcher takes a random sample of 75 college professors and is found to have a mean monthly salary of 19,375 pesos. Do college professors have lower salaries than the rest? Test the claim at a 5% level of significance.

PROBLEM 4 (10 points)

A sample of 70 observations is selected from a normal population. The sample mean is 2.78 and the standard deviation is 0.83. Another sample of 58 observations is selected from a normal population. the mean sample is 2.63 and the sample standard deviation is 0.75. test the hypothesis using a 5% level of significance.