1. 2. 3. 4. Mong Corporation makes auto batteries. The company claims that 80% of its LL70 batteries are god for 70 months or longer. Assume that this claim is true. Let p-hat be the proportion in a sample of such batteries that are good for 70 months or longer. a) What is the probability that the sample proportion will be between 0.76 and 0.83? b) What is the probability that this sample proportion is within 0.05 of the population proportion? Keisha has over 500 songs on her cell phone. She wants to estimate the proportion of songs that are by female artistes. She takes SRS of 50 songs on her phone and finds that 20 of the songs are by female artistes. Create a 99% confidence interval for the proportion of songs on her phone that are by female artistes. The Pepsi Challenged asked soda drinkers to compare Diet Coke and Diet Pepsi in a blind taste test. Pepsi claimed that more than of Diet Coke drinkers said they preferred Diet Pepsi. Suppose we took a random sample of 100 Diet Coke Drinkers and we found that 56 preferred Diet Pepsi. Conduct the appropriate test to determine if Pepsi's claim is true. Kevin wants to estimate the proportion of citizens in a certain area that favour a tax increase. He wants his margin of error to be no more than 2% at the 90% confidence level. What sample size does he need to achieve the margin of error? NB: As stated in the notes, if the estimated value for p is not given, assume p = 0.5 1. The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. a) After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 90% confidence interval for the mean assembly time. b) How many workers should be involved in this study in order to have the mean assembly time estimated up to 15 seconds with 90% confidence? 1 ECON1005: INTRODUCTORY STATISTICS PROBLEM SET 9 2. 3. Researchers are interested in estimating the change in scores on students' second attempt at a certain test. History indicates that the change in scores is normally distributed with a standard deviation of 50. What size sample should the researchers use if they want to be within 2 units of the true value with 95% confidence? Bags of a certain brand of chips claim to have a net weight of 14 ounces but the net weight varies slightly from bag to bag, with a population standard deviation of 0.24. A representative of a consumer advocacy group wishes to see if there is any evidence that the mean net weight is less than advertised. A sample of 16 bags of this brand of chips is found to have a net weight of 13.82. Use these data to perform an appropriate test of hypothesis at 5% significance level.