The hypotheses are: Ο Ho:ρ > 0; Ha:ρ< 0 Ο Ho:ρ< 0; Ha:ρ > 0 O Ho:r > 0; Ha:r < 0 O Ho:r 0; Ha:r + 0 Ho:r < 0; Ha:r > 0 Ο Ho:ρ= 0; Ha:ρ ή 0 2. This is a O twoO rightO left tailed test and the distribution used is OT Oz The Degrees of Freedom are 08 ON/A; this is a Z-test 07 3. The STS (round to 3 decimals) is: The P-value (round to 4 decimals) is:

Consider a random sample of size n from a normal distribution with unknown mean u and unknown variance o?. Suppose the sample mean is X and the sample variance is S?. n = 16, the observed sample mean i is 8.9. the observed sample variance s? is 25 and 4o : 10.5. Suppose we now want to test Ho : o? = of versus H1 : o? + of. Which of these test statistics should we use? Select one: (n-1)s? W = of a. O b. Z %3D O c. T= S/n Let o = 36. What is the (appropriate) observed test statistic? Give answer to three decimal places. What is the p-value of the (appropriate) observed test statistic for testing Ho : o? = of versus H1 : o? + of you just computed? Give answer to three decimal places.

USE THE T-DISTRIBUTION AND THE GIVEN SAMPLE RESULTS TO COMPLETE THE TEST OF THE GIVEN HYPOTHESE S. ASSUME THE RESULTS COME FROM RANDOM SAMPLES, AND IF THE SAMPLE SIZES ARE SMALL. ASSUME THE UNDERLYING DISTRIBUTIONS ARE RELATIVELY NORMAL.                    TEST Ho: MIU 1= MIU 2 VS Ha: MIU1>MIU 2 USING THE SAMPLE RESULTS x̅1= 56  S1= 8.2 WITH N1 = 30 AND x̅ 2= 51, S2=6.9 WITH N2 =40.                                                                                                                                                                                            GIVE THE TEST STATISTIC AND THE P-VALUE                                                                                                                                                                         WHAT IS THE CONCLUSION OF THE TEST ? AT A 5% LEVEL.

The following histogram shows the distribution of 1000 sample observations from a population with a mean of u=4 and a variance of o = 8. 10 Suppose a simple random sample of 100 observations is to be selected from the population and the sample average x is calculated. Which of the following statements about the distribution of is/are FALSE? A) The distribution of x will have a mean of 4. B) The distribution x will be approximately Normal. C) Because the distribution shown in the histogram above is clearly skewed to the right, the shape of the distribution of x will also show skewness to the right. D) Even though the distribution of the population variable appears to be skewed to the right, the distribution of x will be approximately symmetric around u= 4. E) The standard deviation of the distribution of x will be 0.283.

Assume that X has a normal distribution, and find the indicated probability. 7) The mean is μ = 15.2 and the standard deviation is o = 0.9. Find the probability that X is between 14.3 and 16.1. A) 0.1587 B) 0.6826 C) 0.8413 D) 0.3413 7)

4. Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are Normally distributed with mean μ. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses Ho: = 14, Ha: < 14. To do this, he selects 16 bags of this brand at random and determines the net weight of each. A Type I error in this setting would mean (a) concluding that the bags are being underfilled when they actually aren't. (b) concluding that the bags are being underfilled when they actually are. concluding that the bags are not being underfilled when they actually are. (d) concluding that the bags are not being underfilled when they actually aren't. (e) none of these

Use a T-table if necessary.

Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 36. Complete part (a) through (c) below. ..... a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 36. The value of the mean is u = рeas. (Type an integer or a decimal. Do not round.)