Find Py ⬍ 14.61. 7.3 For a

a. If the process yields jars having a normal distribution with a mean of 32.30 ounces and

a standard deviation of .15 ounces, what proportion of the jars filled on the packaging line will be underfilled?

b. Does the plot suggest any violation of the conditions necessary to use the chi-square

procedures for generating a confidence interval and a test of hypotheses about ? c. Construct a 95 confidence interval on the process standard deviation. d. Do the data indicate that the process standard deviation is greater than .15? Use

e. Place bounds on the p-value of the test. Engin.

7.6 A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are travel- ing at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 100 vehicles is selected from a sec- tion of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data are summarized here and in a boxplot. a ⫽ .05. s Descriptive Statistics for Juice Data Variable N Mean Median TrMean StDev SE Mean Juice Jars 50 32.267 32.248 32.270 0.135 0.019 Variable Minimum Maximum Q1 Q3 Juice Jars 31.874 32.515 32.177 32.376 Descriptive Statistics for Vehicle Speeds Variable N Mean Median TrMean StDev SE Mean Speed mph 100 64.48 64.20 64.46 11.35 1.13 Variable Minimum Maximum Q1 Q3 Speed mph 37.85 96.51 57.42 71.05 40 50 60 70 80 90 100 Speed mph

a. Does the boxplot suggest any violation of the conditions necessary to use the chi-square

procedures for generating a confidence interval and a test of hypotheses about ?

b. Estimate the standard deviation in the speeds of the vehicles on the interstate using a

95 confidence interval.

c. Do the data indicate at the 5 level that the standard deviation in vehicle speeds

exceeds 10 mph? s