HP340: Statistical Methods, Spring 2015Due Date: 3:30PM, Tuesday Mar 3, 2015 Homework 6Total Points: 25Show your work/explain your reasoning when calculations are required. Late assignments will not be accepted.1. (13 total points) Based on Xand sXderived from a random sample of size N, you perform a two-sided one-sample t-test and reject the null hypothesis H0: =0 at the 5% significance level. Determine whether the following statements are True, False, or can’t be determined from the information provided. (1 point each).A. The null hypothesis is false. CANNOT BE DETERMINEDB. The alternative hypothesis is true. CANNOT BE DETERMINEDC. It would be unlikely to observe a value as extreme or more extreme than Zobs if the null hypothesis were true. FALSED. A type I error could have occurred. TRUEE. A type II error could have occurred. FALSEF.  is inside the 95% confidence interval given by X ±tcrit´ sX (where tcrit is the 5% critical value of the t-distribution with N-1 df) TRUEG. 0 is outside the 95% confidence interval given by X ±tcrit´ sX(where tcrit is the 5% critical value of the t-distribution with N-1 df) FALSEH. If the null hypothesis were true and we repeated the test many times based on different random samples of size N form the same population, we would reject the null hypothesis about 5% of the time. TRUEI. If the alternative hypothesis were true and we repeated the test many times based on different random samples of size N form the same population, we would reject thenull hypothesis about 100x(1-)% of the time. FALSE J. If you performed the same test based on a sample of size larger than N, the power ofthe test would increase. TRUEK. If you performed the same test based on a sample of size larger than N (also at the 5% significance level) the probability of wrongly rejecting the null hypothesis (i.e. rejecting it when true) would decrease. FALSEL. The p-value is smaller than 0.05 TRUEM. The p-value is smaller than 0.01. CANNOT BE DETERMINED2. (12 points total) To investigate the relationship between dietary cholesterol and blood cholesterol in healthy young adults, researchers measured total cholesterol in a sample of 25 healthy young adults who reported to consume a diet high in dietary cholesterol and 28 healthy young adults who reported to consume a diet low in dietary cholesterol. The 25 subjects in the high dietary cholesterol group had a mean total blood cholesterol of 175mg/dlwith 1s= 15mg/dl, whereas the 28 subjects in the low dietary cholesterol group had a mean total blood cholesterol of 169 mg/dl with 2s= 16. Conduct a two-tailed test at the 5% significance level to investigate whether the mean blood cholesterol is the same among healthy young adults with high and low dietary cholesterol diets. State a brief conclusion based on your findings.High dietary cholesterol sampleN =25,´X =175, s1=15 Low dietary cholesterol sampleN =28,´X =169, s1=16 df=(25+28)-2=51  tcrit=2.000tind=´X1−´X2√[(n1−1)s12+(n2−1)s22n1−n2−2][1n1+1n2]=175−169√[(25−1)15❑2+(28−1)16❑251][125+128]=67.68=0.78|tind|<tcrit -2<tind<2Do not reject null hypothesis at 5% significance level. The difference between the sample means is nonsignificant, and only differs due to sampling error.There is no evidence that either low or high cholesterol diets had any effect on thesample