Answer the follwoing: Statistics and Probability: Hypothesis Testing

A. Read and understand the given statements below. Determine the value of a or "/2 based on the alternative hypothesis in decimal form. Write your answer in mathematical symbol in your notebook. 1. In 2015, it was recorded that around 34% of the population in 2015 were not married. A researcher surveyed a random sample of 500 couples. He found out that 18% of them were living together but unmarried. Test at 5% significance level that the current percentage of unmarried couples is different from 34%. 2. An average construction worker hourly rate pay in the Philippines is Php 62.50 with a standard deviation of Php 6.01. A random sample of 20 manufacturing workers were asked on their hourly rate and found out that they had an average of Php 50 hourly rate pay with a standard deviation of Php 5.00. Construct a 90% confidence interval E that the average hourly rate for construction workers is higher than the average hourly rate for manufacturing workers. 3. A chemist invented an additive to increase the lifespan of rechargeable battery. The said additive will extend on average the battery's lifespan to 48 months. Test the hypothesis at 0.01 level of significance that the average lifespan is higher than 48 months. 4. The average number of years to finish basic education is 14. A sample of 30 senior high school students were asked and found out that the mean number of years to finish their basic education is 12 with a standard deviation of 2 years. Test the hypothesis at 93% confidence interval that the average number of years to finish basic education is less than 14 years. 5. A sample of 100 private school students were surveyed whether they planned to transfer to public school in the incoming school year. Results showed that 40% of these students will transfer to public school. Test the average number of private school students that will transfer to public school is not 40% at 5% level of significance