In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation σ is 2.4 and that the population of height measurements is normally distributed. Construct the 95% confidence interval for the population mean. 1.2. Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677. 1.3. Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. 1.4. A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans. 1.5. The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of 4.2 years. Construct the 98% confidence interval for the population variance. Question 2 2.1. A sample of 500 respondents was selected in a large metropolitan area in order to determine various information concerning consumer behaviour. Among the questions asked was "Do you enjoy shopping for clothing?" of the 240 males, 136 answered "Yes". Of the 260 females, 224 answered "Yes". Is there is evidence that the proportion of females who enjoy shopping for clothing is higher than the proportion of males? Test at 5% level of significance. 2.2. A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean and standard deviation calorie content of this brand of energy bar. Assume that the distribution of the calorie content is approximately normal. Question 3 3.1. A manufacturer of electronic calculators is interested in estimating the fraction of defective units produced. A random sample of 800 calculators contains 10 defectives. Compute a 89% two-sided confidence interval on the fraction defective. 3.2. The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, revealing 13 defectives. Find a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. 3.3. The government is interested in determining the number of manufacturing firms that plan to "fight inflation" by following certain voluntary wage price guidelines. A sample of 100 manufacturing firms is taken, and 20 said that they do not plan to follow any of these guidelines. Determine the 95% confidence interval for the percentage of firms that do plan to follow the guidelines. Page 1 of 2 Lecturer: Mr. JC Kabala 22 September 2022 Question 7 4.1. A rivet is to be inserted into a hole. A random sample of 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is 0.008 millimeters. Construct a 99% confidence interval for σ 2
. 4.2. The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is 0.37. Construct a 95% two-sided confidence interval for σ.