Stats Quiz : 1. Bolts are produced by a certain process. The diameters of the bolts have mean 13cm and standard deviation 0.7cm. The bolts are packaged randomly into packets of 100 bolts. Which of the following is true about the mean diameter of a packet of 100 bolts? The mean diameters of the packets of 100 bolts have a mean of 1.3cm and a standard deviation of 0.7cm. The mean diameters of the packets of 100 bolts have a mean of 13cm and a standard deviation of 0.007cm. The mean diameters of the packets of 100 bolts have a mean of .13cm and a standard deviation of 0.007cm. The mean diameters of the packets of 100 bolts have a mean of 13cm and a standard deviation of 0.07cm. The mean diameters of the packets of 100 bolts have a mean of 0.13cm and a standard deviation of 0.07cm. 2. The proportion of individuals in a large population who have a particular characteristic is pi=0.03. What is the sampling distribution of the sample proportion, P, with this characteristic, from random samples of size n=100? The distribution of P can be well approximated by the normal distribution N(0.03, 0.017 ) The sample size n=100 is too small here for a normal approximation to be a good approximation. The distribution of P can be well approximated by the normal distribution N(0.03, 0.291) The distribution of P can be well approximated by the normal distribution N(0.03. 0.000291 ) The distribution of P can be well approximated by the normal distribution N(0.03,0.17 ) 3 A 95% confidence interval for the true mean lifetime of batteries from a new and cheaper supplier was determined to be (85.5, 93.9) hours. If it is required to have a more accurate (i.e., shorter) confidence interval for the mean, how could this be obtained? By taking a larger sample; or by allowing a lower level of confidence (eg 90%). By taking a smaller sample; or by allowing a higher level of confidence (eg 99%). The length of the confidence interval will be the same regardless of the size sample and the level of confidence. By taking a smaller sample; or by allowing a lower level of confidence (eg 90%). By taking larger sample; or by allowing a higher level of confidence (eg 99%). 4 Suppose you observe a random sample of 13 observations from a normal distribution with unknown mean but known standard deviation =4. Given that the computed sample mean is x=21.05construct a two sided 99%condence interval for and write the endpoints of the interval below (Please write to 2 decimal places): 5. Suppose you observe a random sample of 108 observations and are interested in the proportion of individuals that have a particular characteristic. Given that the computed sample proportion is p=0.25construct a one sided 90%upper condence bound for and write the endpoints of the interval below (Please write to 2 decimal places): 6. Suppose the typical lifespan of a type of chain used in industry was believed to have mean =50months. A sample of the last n=15worn out chains yielded a sample mean of x=51.69and sample sd s=2.05. Assuming that the chain life is normally distributed, conduct a hypothesis test that the mean lifespan of the chains has changed. Do this by assuming a signicance level =0.05and calculating the rejection region below. (a) We reject the null hypothesis if x[ Please write your answers to two decimal places. (b) What decision should be made in this situation? , \f\f\f