1. A random sample of size n = 16 from a normal population yield a sample mean of x = 53.7 and standard deviation s = 23.3.

(a) Construct and interpret a 95% confidence interval for mean .

(b) Suppose that = 20. What sample size is required that our estimate is within 2 units from the mean.

2. Arandomsampleof15shearingpinsistakeninastudyoftheRockwellhardnessofthepinhead.MeasurementsontheRockwellhardnessaremadeforeachofthe15,yieldinganaveragevalueof47.50withasamplestandarddeviationof2.5.Assumingthemeasurementstobenormallydistributed,(a)constructa90%confidenceintervalforthemeanRockwellhardness,and(b)constructa95%predictioninterval.

3.The following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to clear up severe bladder infections:

Medication 1 n1 = 14 x 1 = 17.4 s21 = 1.78

Medication 2 n2 = 16 x 2 = 19.2 s2 = 1.65

Find a 95% confidence interval for the difference 2 1 in the mean recovery times for the two medications, assuming normal populations with equal variances.

1. A study is to be made to estimate the proportion of residents of a certain city and its suburbs who favor the construction of a nuclear power plant near the city.
   1. (a) How large a sample is needed if one wishes to be at least 95% confident that the estimate is within 0.04 of the true proportion of residents who favor the construction of the nuclear power plant?
   2. (b) In a sample of 285 residents it is found that 121 are in favor the construction of the power plant. Construct a 95% confidence interval for the proportion of residents that favor the plant and give its interpretation.
2. Ten engineering schools in the United States were surveyed. The sample contained 250 electrical engineers, 80 being women; 175 chemical engineers, 40 being women. Compute a 90% confidence interval for the difference between the proportions ofwomen in these two fields of engineering. Is there a significant difference between the two proportions?

6. A random sample of size n = 64 from a Poisson random variable with unknown mean yields a sample mean of x = 8.5. Use the central limit theorem to find a 95% confidence interval for .