In order to test the proportion of smokers who agree with the prohibition of smoking in public buildings, a researcher takes: Statistics and Probability Assignment, UMP, Malaysia

University Universiti Malaysia Pahang (UMP)
Subject Statistics and Probability

QUESTION 1
In order to test the proportion of smokers who agree with the prohibition of smoking in public buildings, a researcher takes a random sample of 500 smokers. He found that 155 of them agree that smoking should not be allowed in public buildings.

a) Write the formula for (1— a)100% confidence interval for the true proportion.
b) Calculate the size of maximum error for the 99% confidence interval.
c) Obtain a 99% confidence interval for the population proportion of smokers who think that smoking should not be allowed in public buildings.

QUESTION 2
A publishing company has published a reference book. The company collected information on the prices of 16 similar reference books in order to determine an appropriate price for its book. The sample givesmeanRM 70.50 and a standard deviation of RM 4.50. Assume the price is normally distributed.

a) Suppose T: is chosen as a point estimate for the population mean. Show that this estimator is unbiased.

b) Determine the sampling distribution for the sample mean..V:

c) Calculate the 95% confidence interval for the population mean price for the reference books. What is your conclusion?

QUESTION 3
13 Two years ago, 75% of a financial bank’s customers were satisfied with the service provided by the bank. The bank manager would like to test if the percentage has changed over time.

a) What hypothesis should be tested?
b) From a survey on 20 random samples, 13 customers are satisfied. Determine the rejection region at a.
c) Calculate-value.
d) If the probability of incorrectly rejecting a true lic, is 0.01, what decision shall you obtain?

QUESTION 4
A type of treatment has been identified to produce cement compression strength of 5000 kg/cm2 with a standard deviation of 120. To test the null hypothesis that p = 5000 against the alternative hypothesis that pc 5000, a random sample of 50 pieces of cement was tested. The rejection region is defined as x <4970.

a) Define Type I and Type II Error for the testing.

b) Calculate the probability of Type II Error if p= 4960.

c) What is the power of the test?

QUESTION 5
A salesman for a brand of mobile phones dams that its phone is cheaper and the phone better than another brand. To test this statement, a random sample is taken and summaries are given in the following table. Product Number Defective Number Checked Salesman 15 150 Other brand 6 150

a) State the null and alternative hypotheses.

b) Calculate the test statistics.

c) Give a conclusion at the 0.05 level of significance.

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