Statistics and Probability Answers

It is claimed that the mean annual salary of call center customer service representative is php 188 584.00. A researcher randomly selected 45 call center customer service representative. He computed the mean of their annual salaries and obtained a mean of php 188 600.00. Does this show that the mean salary of call center customer service representatives is greater than php 188 584.00? Use 0.05 level of significance and assume that the population standard deviation is php 39.50.

A company which produces batteries claims that the life expectancy of their batteries is 90 hours in order to test the claim a consumer interest group tested a random sample of 40 batteries. The test resulted to a mean life expectancy of 87 hours. Using a 0.05 level of significance, can it be concluded that the life expectancy of their batteries is less than 90 hours? Assume that the population standard deviation is known to be 10 hours.

The head of the math department announced that the mean score of grade 11 students in the first periodic examination isn mathematics was 89 and the standard deviation was 12. One student believed that the mean score was less than this, randomly selected 34 students and computed their mean score. She obtained a mean score of 85. At 0.01 level of significance, test the students belief.

A medical practitioner wants to estimate the mean systolic blood pressure in pre-school children with inbom heart disease. He plans on using a 99% confidence interval and a margin of error of 5 units. The standard deviation of systolic blood pressures in pre-school children with inborn heart disease is 20. How many children should be enrolled in the study?

An Environmentalist is making a survey on the number of households that applies the principles of Waste Management in a certain community. Given the standard deviation of 26, how large a sample must be selected if we want to be 95% confident of finding whether the true mean differs from the sample mean by 1.5 hour?

What is the probability of both coins landing on heads?

Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company

states that the drug is equally effective for men and women. To test this claim, they choose a

simple random sample of 110 women and 190 men from a population of 100,000 volunteers.

At the end of the study, 28% of the women caught a cold; and 61% of the men caught a cold.

Based on these findings, can we reject the company's claim that the drug is equally effective for

men and women? Use a 0.05 level of significance.

The manager of Penawar Chemical Company claims that their major product contains on average u = 3.0 fluid Ounces of acid material per gallon. If there is too much acid material, the product will be too dangerous. A quality inspector was brought in to test the product. She randomly selected a sample of 100 gallon-size containers of the product. The results were as follow. Mean weight Frequency 2.80 10 2.90 6 3.00 30 3.10 54 SUM 100

d. Using a 5% significance level, explore the critical point. Hence, write the decision rule. [2 marks) e. At the 5% level of significance, investigate whether there is sufficient evidence to support the Company's claim. Assume the acid materials fluid Ounces per gallon are normally distributed. What is your expectation about the company product? (5 marks)

The manager of Penawar Chemical Company claims that their major product contains on average u = 3.0 fluid Ounces of acid material per gallon. If there is too much acid material, the product will be too dangerous. A quality inspector was brought in to test the product. She randomly selected a sample of 100 gallon-size containers of the product. The results were as follow. Mean weight Frequency 2.80 10 2.90 6 3.00 30 3.10 54 SUM 100 d. Using a 5% significance level, explore the critical point. Hence, write the decision rule. [2 marks) e. At the 5% level of significance, investigate whether there is sufficient evidence to support the Company's claim. Assume the acid materials fluid Ounces per gallon are normally distributed. What is your expectation about the company product? (5 marks)

a random sample of 81 items is taken, producing a sample mean of 47. The population standard deviation is 5.89. construct a 90 confidence interval to estimate the population mean.