Exercises. 1. In each case, find the number b so that

1. In each case, find the number b so that

a) when n =7

b) when n =16

c) when n =9

d) when n =12

2. For each of the following, find the area in the appropriate tail of the t distribution

a)

b)

c)

d)

3. Find the value of t from t – distribution table for each of the following:

a) Confidence level = 99 % and d. f. =18

b) Confidence level = 95 % and n =26

c) Confidence level = 90 % and d. f. =15

4. The mean number of the sample of 25 bolts produced on a specific machine per day was found to be 47 with a standard deviation of 2.4. Assume that the number of bolts produced per day on this machine has a normal distribution.

Construct a 90 % confidence interval for the population mean .

5. A random sample of 16 cars, which were tested for fuel consumption, gave a mean of 26.4 miles per gallon with a standard deviation of 2.3 miles per gallon. Assuming that the miles per gallon given by cars have a normal distribution, find a 99 % confidence interval for the population mean .

6. A sample of eight adults was taken, and these adults were asked about the time they spend per week on sport activities. Their responses (in hours) are as follows:

45; 12; 31; 16; 28; 14; 18; 26

Make a 95 % confidence interval for the mean of time spent per week by all adults on sport activities.

7. A sample of 10 customers who visited a supermarket was taken. The following data give the money (in dollars) they spent during that visit:

74; 89; 121; 63; 146; 47; 91; 28; 84; 76

Assuming that the money spent by all customers at this supermarket has a

normal distribution, construct a 90 % confidence interval for the population mean.

8. The mean time taken to design a home plan by 20 designers was found to be 185 minutes with a standard deviation of 23 minutes. Assume that the time taken by all designers this home plan is normally distributed.

Construct a 99 % confidence interval for the population mean .

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