Exercises. 1. A random sample of size 10 from a normal population with variance 50 gave a mean 43.2

1. A random sample of size 10 from a normal population with variance 50 gave a mean 43.2. A second random sample of size 18 from a normal population with variance 72 gave a mean 48.7. Find a 99 per cent confidence interval for the difference between two population means.

2. A random sample of size 100 yielded the sample values

. A random sample size 100 from another population yielded

. Find a 95 % confidence interval for .

3. An urban planning group is interested in estimating the difference between mean household incomes for two cities. Independent samples of households in two cities provide the following results:

City 1 City 2

Develop an interval estimate of the difference between mean incomes in the two cities. Show the results for confidence coefficients of 0.90 and 0.95.

4. The management at the National Bank investigates mean waiting time for all customers at its two branches. They took a sample of 200 customers from the branch A and found that they waited an average of 4.60 minutes with a standard deviation of 1.2 minutes before being served. Another sample of 300 customers taken from the branch B showed that these customers waited an average of 4.85 minutes with a standard deviation of 1.5 minutes before being served. Make a 97 % confidence interval for the difference between the two population means.

5. Rural and urban students are to be compared on the basis of their scores on a nationwide university entrance test. Two random samples of sizes 80 and 95 are selected from rural and urban students. The summary statistics from the test scores are

	Rural	Urban
Sample size Mean Standard deviation	78.6 9.1	85.7 8.3

Establish a 96 % confidence interval for the difference in population mean scores between urban and rural students.

6. A business consultant wanted to investigate if providing day care facilities on premises by companies reduces the absentee rate of working mothers from companies that provide day care facilities on premises. Sample of 50 mothers selected from the companies that provide day care facilities was taken. These mothers missed an average of 6.4 days from work last year with a standard deviation of 1.20 days. Another sample of 50 such mothers taken from companies that do not provide day care facilities on premises showed that these mothers missed an average of 9.3 days last year with a standard deviation of 1.83 days. Construct a 98 % confidence interval for the difference between the two population means.

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