1. A sample of 70 observations is selected from a normal population. The sample mean is 2.77 and a sample standard deviation is 0.82. Another sample of 58 observations is selected from a normal population. The mean sample is 2.63 and a sample standard deviation of 0.75. Test the hypothesis that Ho :mean 1 = mean 2 H1: mean 1 mean 2 = 0.05

2. To compare the NU's Math knowledge in two Department of COE ( CE and ECE ), Mr X got a sample of 27 CE freshmen and 25 ECE freshmen. Both sample were given examination. The results: CE mean score = 85.85 with SD = 7.5 ECE mean score = 90.2 with SD = 10.4 Is there a significant difference between the means? Use = 0.01

3. Independent random samples were selected from two populations and the data is given: Sample 1 mean1 = 253 SD1 = 23 n = 40 Sample 2 mean2 = 240 SD2 = 21 n = 45 Is there a significant difference between the means?

4. A farmer randomly selected 20 matured calamansi tree of one variety. The mean height = 10.7 ft with and SD of 1.24 ft. A 12 randomly selected calamansi tree of another variety have a mean height of 9.5 ft with an SD of 1.46 ft. Is there a significant difference between the two sample means. Use = 0.05.

5. It is believed that no more than 40% of students at the college of Law wear glasses. Of 64 students surveyed, 40 are found to wear glasses. Does this contradict the belief that no more than 40% of the students wear glasses? Use = 0.05.

6. An opinion survey in Town A found that 73% of people considered Nora Aunor should be given the National Artist Award. A random sample of 30 people in town B were asked the same question. 17 thought Nora Aunor should be given the National Artist award. Is this proportion significantly different from town A? Use = 0.05.

7. A sample of Liberal Party and a sample of UNA were polled if they are in favor of Reproductive health bill. Of 200 LP , 90 voted yes on the issue. Of 100 UNA 58 voted yes. Is there a significant difference in how the LP and UNA voted? Use = 0.05

8. The Marketing Department of a detergent company that makes brand TIDES found in a random sample of 200 housewives that 20% favored brand TIDES over all others. After an intensive ad campaign, another sample of 300 housewives showed that 27% favored TIDES. Can the owner of the company conclude that the ad campaign was successful? Use = 0.05.