# 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**

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 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 of 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 errors 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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