11 pts Consider sample mean Xbar. We know that the mean E(Xbar)= and Var(Xbar) = construct Zscore by Z= (X)n to test the null hypothesis H0: 2n. We =0. Which of the following statement is untrue? We can use Z-score as the test statistic irrespective of the sample size. We can use Z-score as the standardized test statistic in part because the sampling distribution is approximately N(0,1), as guaranteed by the central limit theorem. We can use Z-score as a standardized test statistic in part because we can easily determine a critical region and its associated significance level based on the N(0,1) distribution. We can use Z-score as a standardized test statistic in part because we can easily compute pvalue using N(0,1) distribution. Question 21 pts In testing the null hypothesis H0: p0<0.3 vs. Ha: p>0.3. Which critical region is incorrect? Certain values of sample proportion that are smaller than 0.3: Z=(p-hat-0.3)/ < 1.64 Certain values of sample proportion that are greater than 0.3: Z=(p-hat-0.3)/ > 1.64 Certain values of sample proportion that are greater than 0.3: Z=(p-hat-0.3)/ >2.53 Certain values of sample proportion that are either smaller than 0.3 or greater than 0.3: |Z|=|(p-hat 0.3)/ |> 1.64 A and D Question 31 pts In a random sample of size 100 students, sixty used Facebook daily in the past week. Assuming that under a null hypothesis the true population proportion of regular use of Facebook is 65%, what is the observed value of Zscore for this observed sample? -1.10 -1 -1.05 1.05 Question 41 pts Continue from Q3. If we want to use this random sample to test the hypotheses Ho: p = 0.65 (Null) Ha: p > 0.65 (Alternative) What would be the observed "critical region" to compute pvalue? Z>-1.05 |Z|>1.05 (that is, Z<-1.05 or Z>1.05) Z>1.05 Cannot be determined. Question 51 pts Which of the following statement about pvalue is NOT true? p-value is the probability of observing any value that is at least as inconsistent to H as the observed test value. p-value is predetermined before we conduct the experiment or obtain a sample p-value serves as the actual significance level at which the observed data are against the null hypothesis If p-value is less than a nominal level , then we can reject the null hypothesis at -level. 0 Question 61 pts From time to time we update our knowledge about the prevalence of current medication allergy. In a random sample of 100 adults, 15 people reported a particular allergy. Using this sample what would be the pvalue of your test of the following hypotheses and the conclusion? (Note: this is a twosided alternative so the critical region is on both right and left tails) Ho: p = 0.10 (Null) Ha: p 0.10 (Alternative) (hint: twotailed critical region for pvalue) p-value=0.096, reject the null at significance level 0.01 p-value=0.096, fail to reject the null hypothesis at alpha-level 0.05 p-value=0.016; reject the null hypothesis at alpha-level 0.05 p-value=0.016; fail to reject the null at alpha=0.01 Questions 710 are related to this question Three hundred eighty patients were recruited to participate in a clinical trial to test the efficacy of a new antianxiety medication. These patients were randomly assigned to either medication or placebo. Among n1=200 people taking the medication 136 achieved targeted symptom reduction whereas among n2=180 people receiving placebo, 92 reported symptom reduction. Let p1 and p2 be the true proportion of symptom response. We want to test the hypotheses H0: p1=p2 Ha: p1>p2 Question 71 pts Under the null hypothesis p1=p2, what would be the common sample proportion of symptom reduction when the two groups are pooled? 0.55 0.60 0.42 0.56 Question 81 pts To test the null hypothesis, the Zscore is given by Z=(p1_hat p2_hat)/sqrt(p(1p)(1/n1 + q/n2) where p is the pooled proportion from Q7. Calculate the observed Zscore from the given data. 3.00 3.30 3.36 3.44 Question 91 pts Using ovserved zscore given in Q8, pvalue=Pr(Z>z) for testing against the null hypothesis is computed using N(0,1) distribution. Which of the following is correct? p-value=0.00039 p-value = 0.05 p-value = 0.01 p-value = 0.001 Question 101 pts Based on the calculation, we will reject the null hypothesis at a significance level 0.0001 0.001 0.01 0.05 Questions 11 to 13 are based on following information: To compare the treatment effect of two medications, performance data were collected on two independent samples of patients. The investigators decided to conduct a twosample ttest for the difference in mean with the following hypotheses. H0: u1u2=0 vs H1: u1u2 0 They found that the difference between the two sample means was 3.3. The sample standard deviation of the first sample is 4.6 with a sample size of 16 and the standard deviation of the second sample is 4.8 with a sample size of 18. Question 111 pts What would be the observed value of the Tscore under the null hypothesis? 1,04 1.54 2.04 2.64 Question 121 pts What is the degrees of freedom for the underlying tdistribution? 33 32 34 Question 131 pts What would be the pvalue? 0.050 0.025 0.021 0.042