Chaper 11, 12, 13

Samples from two independent, normally distributed populations produced the following results. P1 P2 Sample Size 7 9 Sample Mean 15.9 12.6 Sample SD 10.2 13.4 Calculate the 95% confidence interval for the difference between population means, (u1-u2). A. (-9.65, 15.65) B. (-8.26, 14.86) C. (-10.10, 16.74) D. (-0.55, 2.54)

A. (-9.65, 15.65)

Karl is a software developer who is interested in determining whether two random number generators have the same population mean. Random number generator A has a population standard deviation of 1.00 and random number generator B has a population standard deviation of 1.25. Karl took a sample of 10 trials from each generator. The results are summarized below. RNG A: -1.544, -1.327, 0.668, -0.997, 1.717, 0.678, -0.230, -0.040, -0.125, 1.167 RNG B: -0.399, 1.288, -0.294, 1.639, 2.174, 0.683, 0.123, -1.096, 1.931, 0.869 Find the P-value for the test of the difference between the population means for these two generators. A. 0.171 B. 0.169 C. 0.086 D.0.095

A: 0.171

A study is conducted to determine whether the proportion of airline passengers complaining with post-flight respiratory symptoms is larger for flights that do not circulate cabin air that for flights that do circulate the air. After checking to make sure that all of the necessary conditions were met, we calculated the value of the z test statistic to be z=0.84. Which of the following is the P-value associated with this test?

B. 0.2005

For which of the following samples sizes and p-hat would it be appropriate to use p1-p2+/-(z critical value)(p1(1-p1))n1+p2(1-p2)n2 to estimate a difference in population proportion. 1. n1=n2=100; p1=0.09; p2=0.12 2. n1=n2=100; p1=0.71; p2=0.69 3. n1=n2=300; p1=0.98; p2=0.96

B. 2 only

A packaging machine is supposed to fill boxes of breakfast cereal to a weight of 16 ounces. Eight filled boxes are selected at random and the weight of cereal is determined. The results (in ounces) are summarized in the following table. 16.7, 16.0, 16.4, 15.9, 16.5, 16.2, 15.9 A technician wishes to test the claim that the machine is overfilling the boxes. At the 5% significant level, what is the p-value of the test statistic? A. 0.262 B. 0.005 C. 0.032 D. 0.081 E. 0.115

C. 0.032

A study determined that in 2009, 38% of those in a random sample of 100 adult Americans had accounts with some type of social web site. In a similar survey conducted in 2012, 53% reported having accounts. Suppose that the 2012 figure was also based on a random sample of size 100. The 95% confidence interval for the difference in population proportions (p2012-p2009) is:

C. 0.15+/-0.136

The spread of the sample mean decreases when: A. The population mean increases B. The population sd increases C. The sample mean decreases D. The sample size decreases E. The sample size increases

E. The sample size increases

True or False: A t-curve is bell-shaped like the z-curve but is less spread out.

False

True or False: The distribution of (x-mean) will always have the same shape as the distribution of the population being sampled.

False

True or False: When testing a hypothesis concerning the difference of two independent population means, if the variance of the difference is estimated using the sample variances, the resulting test statistic has a Normal distribution.

False

True or False: (x1-mean)-(x2-mean) is an unbiased statistic that is used to estimate (u1-u2).

True

True or False: The distribution of (x-mean) is normal if the population is normal.

True

True or False: The hypothesis p1=p2 is equivalent to the hypothesis p1-p2=0.

True

True or False: The number of degrees of freedom used in the two-sample t-test for independent samples are the same as the degrees of freedom used in the construction of a confidence interval for (u1-u2).

True

True or False: Two samples are said to be independent when the selection of the individuals in one sample has no bearing on the selection of those in the other sample.

True