to} Draw a t-distribution with the area that represents the P-value shaded. Choose the correct graph below. {3:- A. C: B. C: C. i' '2 D. a a a a q q q q D\" D\" D\" D\" 73 O 3 73 O 3 73 O 3 73 O 3 {d} Approximate and interpret the P-value. The probability of observing a 7 statistic V the one observed, assuming 7 is true, is in the range V {e} If the researcher decides to test this hypothesis at the or = 0.01 level of significance, will the researcher reject the null hypothesis? Why? Because the P-value is Y than a, the researcher will V the null hypothesis. {f} Construct a 99% confidence interval to test the hypothesis. The lower bound is The upper bound is . Round to three dec'mal places as needed.) Because the value lies V the condence interval, we V the null hypothesis. Type an integer or decimal. Do not round.) The average daily volume ofa computer stock in 2011 was p = 35.1 million shares, according to a reliable source. Astock analyst believes that the stock volume in 2018 is different from the 2011 level. Based on a random sample of 30 trading days in 2018, he finds the sample mean to be 31.1 million shares, with a standard deviation of s = 12.9 million shares. Test the hypotheses by constructing a 95% condence interval. Complete parts (a) through (0) below. HO: V V 35.1 million shares H1: V V 35.1 million shares (b) Construct a 95% condence interval about the sample mean ot stocks traded in 2018. With 95% confidence, the mean stock volume in 2018 is between million shares and million shares. (Round to three decimal places as needed.) {0} Will the researcher reject the null hypothesis? C) A. Reject the null hypothesis because u = 35.1 million shares falls in the condence interval. [:3 B. Do not reject the null hypothesis because u = 35.1 million shares tails in the condence interval. C? C. Do not reject the null hypothesis because u = 35.1 million shares does not fall in the condence interval. (:3. D. Reject the null hypothesis because u = 35.1 million shares does not tall in the confidence interval. A college entrance exam company determined that a score of 23 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 200 students who completed this core set of courses results in a mean math score of 23.2 on the college entrance exam with a standard deviation of 3.4. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 23 on the mathematics portion of the exam? Complete parts a) through d) below. a) State the appropriate null and alternative hypotheses. Fill in the correct answers below. The appropriate null and alternative hypotheses are H0: V V versus H1: V V b) Verify that the requirements to perform the test using the t-distribution are satisfied. Check all that apply. The students were randomly sampled. A boxplot of the sample data shows no outliers. The sample size is larger than 30. The sample data come from a population that is approximately normal. The students' test scores were independent of one another. 319133.090? None of the requirements are satised. c] Use the P-value approach at the a = 0.10 level ot Signicance to testthe hypotheses In part (a). Identify the test statistic. To = (Round to two decimal places as needed.) Identify the P-value. P-Value = (Round to three decimal places as needed.) d) Write a conclusion based on the results. Choose the correct answer below. V the null hypothesis and claim that there V sufcient evidence to conclude that the population mean is than 23. To test H0: u = 42 versus H1: u #42, a simple random sample of size n = 35 is obtained. Complete parts (a) through (1') below. Click the icon to View the table of critical t-Values. {a} Does the population have to be normally distributed to test this hypothesis by using t-distribution methods? Why? [:3 A. Yesthe population must be normally distributed in all cases in order to perform a hypothesis test. L: B. Nothere are no constraints in order to perform a hypothesis test. U C. Yessince the sample size is at not least 50, the underlying population does not need to be normally distributed. L? D. Nosince the sample size is at least 30, the underlying population does not need to be normally distributed. {b} If)? = 45.7 and s = 8.9, compute the test statistic. to = (Round to two decimal places as needed.)