(a) Write the appropriate hypotheses. (b) Check the necessary assumptions. (c) Perform a test withα= 0.1, showing all steps, and report the p-value.
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When drilling for oil in west Texas, about33%of the pilot holes find exploitable oil resources. A local high school student claims that she has built a device that is better at finding oil reserves than the commonly used technology. She reports finding15exploitable wells on 33 pilot holes. What do you conclude about her claim? Explain your answers in all cases.
(a) Write the appropriate hypotheses.
(b) Check the necessary assumptions.
(c) Perform a test withα= 0.1, showing all steps, and report the p-value.
(d) Explain what the p-value means in this context.
(e) Would you invest in the device she created? Explain your reasoning.
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- Suppose that a political campaign by Loki estimates that the candidate’s polling percentage yand the amount x (in hundred thousands of pesos) that is spent on television advertising arerelated by y = e^0.3x + (5lnx)^2 while the amount that is spent on social media advertising are related by (x −3)^4 + 3y = x. (a) If P300,000 has been spent on television advertising by Loki’s campaign, determine therate of spending that will increase his polling percentage by 2 percentage points per week. (b) Suppose that Loki’s political adversary, Thor, is slowly ramping up his presence on socialmedia. If Loki’s team plans on spending P400,000 on social media advertising and the rateof spending is at P100,000 per week, at what rate will the polling percentage increase?Administrators at the stock exchange claim that only 8% of all companies report incorrect higher profits, but you suspect that the proportion is much higher. Use the results of the audit of 200 companies with results that 30 reported incorrect higher profits to answer the following. a. State the null and alternative hypotheses. b. Check to be sure that we are allowed to use Normal calculations. c. Complete the Test on calculator. Report the test statistic value and the p-value. d. State your conclusion regarding the results of your hypothesis test in context of the problem. How many companies should have been audited at 95% confidence level in order for the margin of error to be 3%? Use p=0.08 in your formula. Show all work. Round appropriately e.(i) State the hypotheses, identify the claim with the correct hypothesis, and determine whether it is a one-tailed or two-tailed test. (ii) Find the P-value. Round the answer to at least four decimal places. (iii) Make the decision and summarize the results.
- You may need to use the appropriate appendix table or technology to answer this question. An agency reports that 11.5% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership. (a) Formulate the hypotheses that can be used to determine whether union membership has increased. H0: p = 0.115 Ha: p ≠ 0.115 H0: p > 0.115 Ha: p ≤ 0.115 H0: p ≤ 0.115 Ha: p > 0.115 H0: p ≥ 0.115 Ha: p < 0.115 H0: p < 0.115 Ha: p ≥ 0.115 (b) If the sample results show that 42 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At ? = 0.05, what is your conclusion? - Reject H0. There is sufficient evidence to conclude that there has been an increase in union membership. -…a. State the hypotheses and identify the claim. b. Find the critical value c. Compute the test value. d. Make the decision e. Summarize the results. Undergraduate Enrollment It has been found that 85.6% of all enrolled college and university students in the United States are undergraduates. A random sample of 500 enrolled college students in a particular state revealed that 420 of them were undergraduates. Is there sufficient evidence to conclude that the proportion differs from the national percentage? Use a=0.05Write the null and alternative hypotheses you would use to test each of the situations in parts (a) through (c). (a) A dictator is concerned about his "negatives," that is, the percentage of the country's residents who express disapproval of his job performance. His political committee pays for a series of TV ads, hoping that they can keep the negatives below 44%. They will use follow up polling to assess the ads' effectiveness. Let p be the proportion of the country's residents who express disapproval of the dictator's performance. Ho: P HA: P 0.44 0.44 (b) Is a ten-section spinner fair? Let p represent the probability of the spinner landing on any particular section. Ho: P HA P 1 10 Ho: P HAP 10 (c) Only about 19% of people who try to gain self-confidence succeed. Sellers of a motivational tape claim that listening to the recorded messages can help people succeed. Let p be the proportion of people who try to gain self-confidence and succeed. 0.19 0.19
- According to the Centers of Disease Control, about 21% of American young people between the ages of 12 and 19 are obese. A student claims that the students his local schools are in better shape than the national average, so their proportion of obese students is less than 21%. Which are the appropriate null and alternative hypotheses for this study? Họ: p = 21%, H1: p = 21% Ho: p × 0, Hq: p = 0 Họ: p = 21%, Hq: p > 21% Họ: p = 21%, H,: p < 21% Suppose tnat the result of the statistical is to fail to reject Ho. Which is the proper conclusion? O There is not sufficient evidence to conclude that the students at his local schools have a smaller true proportion of obese students. O There is sufficient evidence to conclude that the students his local schools have a smaller true proportion of obese students. O There is not sufficient evidence to conclude that the students at his local schools have a smaller sample proportion of obese students. O There is sufficient evidence to conclude that…According to a report, the mean of monthly cell phone bills was $49.36 three years ago. A researcher suspects that the mean of monthly cell phone bills is higher today. (a) Determine the null and alternative hypotheses. (b) Explain what it would mean to make a Type I error. (c) Explain what it would mean to make a Type II error. . .. (a) State the hypotheses. Ho: $4 H1: (Type integers or decimals. Do not round.) (b) Explain what it would mean to make a Type I error. Choose the correct answer below. O A. The sample evidence did not lead the researcher to believe the mean of the monthly cell phone bill is less than $49.36, when in fact the mean of the bill is less than $49.36. O B. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is less than $49.36, when in fact the mean of the bill is $49.36. OC. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is higher than $49.36, when in fact the mean of the bill is…You may need to use the appropriate appendix table or technology to answer this question. Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 70 loans approved by Carl (21 of which defaulted) and 80 loans approved by Norm (17 of which defaulted). (a) State the hypothesis test that the default rates are the same for the two loan officers. (Let p1 = the population proportion of Carl's loans that default, and let p2 = the population proportion of Norm's loans that default. Enter != for ≠ as needed.) H0: Ha: (b) What is the sample default proportion for Carl? What is the sample default proportion for Norm? (c) Use a 0.05 level of significance. Calculate the test statistic. (Use p1 − p2. Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.)…
- You may need to use the appropriate appendix table or technology to answer this question. An agency reports that 11.3% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership. (a) Formulate the hypotheses that can be used to determine whether union membership has increased. H0: p ≥ 0.113Ha: p < 0.113 H0: p ≤ 0.113Ha: p > 0.113 H0: p < 0.113Ha: p ≥ 0.113 H0: p = 0.113Ha: p ≠ 0.113 H0: p > 0.113Ha: p ≤ 0.113 (b) If the sample results show that 42 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At α = 0.05,what is your conclusion? Do not reject H0. There is insufficient evidence to conclude that there has been an increase in union membership. Reject H0. There is…You may need to use the appropriate appendix table or technology to answer this question. An agency reports that 11.5% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership. (a) Formulate the hypotheses that can be used to determine whether union membership has increased. H0: p = 0.115 Ha: p ≠ 0.115 H0: p > 0.115 Ha: p ≤ 0.115 H0: p ≤ 0.115 Ha: p > 0.115 H0: p ≥ 0.115 Ha: p < 0.115 H0: p < 0.115 Ha: p ≥ 0.115 (b) If the sample results show that 36 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At ? = 0.05, what is your conclusion? Do not reject H0. There is insufficient evidence to conclude that there has been an increase in union…Evolution and Scientists. A professor claims that more than 83% of all scientists believe in evolution. In a 2014 Pew Research survey of a representative sample of 162 scientists connected to the American Association for the Advancement of Science (AAAS), 146 of these scientists say they believe in evolution. Perform a hypothesis test of the professor's claim using these data.(a) Select the correct null and alternative hypotheses. Ho: p = 0.83Ha: p ≠ 0.83 Ho: p = 0.9Ha: p ≠ 0.9 Ho: p = 0.83Ha: p > 0.83 Ho: p = 0.9Ha: p > 0.9 Ho: p = 0.83Ha: p < 0.83 Ho: p = 0.9Ha: p < 0.9 (b) Find the p-value (round to 4 decimals). (c) Decide whether or not to reject the null hypothesis when α=0.05α=0.05. Fail to reject null hypothesis Reject null hypothesis (d) You should decide that ... there is not enough evidence at α=0.05α=0.05 that more than 83% of scientists believe in evolution. there is enough evidence at α=0.05α=0.05 that more than 83% of scientists believe in evolution.
