6 . ( TCO C ) The manufacturer of a certain brand of toothpaste claims that a high percentage of dentists recommend the use of their toothpaste . A random sample of 400 dentists results in 310 recommending their toothpaste .
a . Compute the 99 % confidence interval for the population proportion of dentists who recommend the use of this toothpaste .
b . Interpret this confidence interval . c . How large a sample size will need to be selected if we wish to have a 99 % confidence interval that is accurate to within 3 %? ( Points : 18 )
7 . ( TCO D ) A Ford Motor Company quality improvement team believes that its recently implemented defect reduction program has reduced the proportion of paint defects . Prior to the implementation of the program , the proportion of paint defects was . 03 and had been stationary for the past 6 months . Ford selects a random sample of 2,000 cars built after the implementation of the defect reduction program . There were 45 cars with paint defects in that sample . Does the sample data provide evidence to conclude that the proportion of paint defects is now less than . 03 ( with a = . 01 )? Use the hypothesis testing procedure outlined below .
a . Formulate the null and alternative hypotheses . b . State the level of significance .
c . Find the critical value ( or values ), and clearly show the rejection and nonrejection regions .
d . Compute the test statistic . e . Decide whether you can reject Ho and accept Ha or not .
f . Explain and interpret your conclusion in part e . What does this mean ?
g . Determine the observed p-value for the hypothesis test and interpret this value . What does this mean ?
h . Does the sample data provide evidence to conclude that the proportion of paint defects is now less than . 03 ( with a = . 01 )? ( Points : 24 )
8 . ( TCO D ) A new car dealer calculates that the dealership must average more than 4.5 % profit on sales of new cars . A random sample of 81 cars gives the following result .