(ii) Test the claim at a 5% significance level using a critical value approach.
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- Two professors at a local college developed a new teaching curriculum designed to increase students' grades in math classes. In a typical developmental math course, 53% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 15 students enrolled, 10 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the a = 0.05 level of significance? Complete parts (a) through (g). (b) Verify that the normal model may not be used to estimate the P-value. npo (1 - Po) : (Round to one decimal place as needed.) Весause = 3.7 < 10, the normal model may not be used to approximate the P-value. (c) Explain why this is a binomial experiment. There is a fixed number of trials with two mutually exclusive outcomes. The trials are independent and the probability of success is fixed at 0.53 for each trial. (Type an integer or a decimal. Do not round.) (d) Determine the P-value using the binomial probability distribution.…Two professors at a local college developed a new teaching curriculum designed to increase students' grades in math classes. In a typical developmental math course, 51% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 18 students enrolled, 13 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the a= 0.05 level of significance? Complete parts (a) through (g). ..... (a) State the appropriate null and alternative hypotheses. 0.51 versus H: p Но (Type integers or decimals. Do not round.) > 0.51 %D (b) Verify that the normal model may not be used to estimate the P-value. Because npo (1- Po) = 4.5 > 10, the normal model may not be used to approximate the P-value. (Round to one decimal place as needed.) (c) Explain why this is a binomial experiment. There is a fixed number of trials with two mutually exclusive outcomes. The trials are independent and the probability of success is fixed at…An airline company is interested in improving the customer satisfaction rate from the 74% currently claimed. The company sponsored a survey of 176 customers and found that 139 customers were satisfied. What is the test statistic z? Ex: 2.22 What is the p-value? Ex: 0.123 Does sufficient evidence exist that the customer satisfaction rate is higher than the claim by the company at a significance level of a = 0.01? Ex: yes or no
- Spam: A researcher reported that 71.8 % of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 69%. He examines a random sample of 500 emails received at an email server, and finds that 365 of the messages are spam. Can you conclude that greater than 69% of emails are spam? Use both a=0.01 and a= 0.05 levels of significance and the critical value method with the table. Part 1 of 5 State the appropriate null and alternate hypotheses. Ho: P- .69 H1: p> .69 This hypothesis test is a right-tailed V test. Part 2 of 5 Find the critical values. Round the answers to three decimal places. For a=0.01 , the critical value is 2.326 For a=0.05 , the critical value is 1.645 Part: 2/5 Part 3 of 5 Compute the test statistic. Do not round intermediate calculations. Round the answer to two decimal places.You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly less than 0.66. You use a significance level of a=0.001. H0:P=0.66 H1:P<0.66You obtain a sample of size 176 in which there are 99 successes.What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)What is the p-value for this sample? (Report answer accurate to 4 decimal places.)This test statistic leads to a decision to reject the null accept the null fail to reject the null As such, the final conclusion is that there is sufficient evidence to conclude that the proportion of women over 40 who regularly have mammograms is less than 0.66. there is not sufficient evidence to conclude that the proportion of women over 40 who regularly have mammograms is less than 0.66. there is sufficient evidence to conclude that the proportion of women over 40 who regularly have mammograms is equal to 0.66. there is not sufficient evidence…Is this p-value significant at the 10% significance level? Is it significant at the 5% significance level? Compare the answers to these questions to your answers to parts (g) and (i) in two complete sentences.
- (d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.) and (e) At the 0.10 level, can the owner conclude that the mean daily sales of the two stores differ? Yes NoIn a test of HO: p = 0.50 vs. HA: p > 0.50, which of the following describes the decision rule at the 5% level of significance. I. Reject HO if the p-value is more than 0.05. II. Reject HO if the p-value is less than 0.05. II. Reject HO if the test statistic is more than 0. %3DA new method was developed to reduce variability of test scores by eliminating lower scores. Two groups, one called the control group and the other, the experimental group, both took the same test. The experimental group was taught using the new method. Do the data provide sufficient evidence to conclude that there is less variation among scores when the new method is used? Perform an F-test at the 1% significance level. (Note: s, = 6.3 and Control Experimental 30 19 29 26 33 36 29 18 33 31 S2 = 3.3.) 33 18 19 32 27 32 29 30 33 ... .. First find the null and alternative hypotheses. Which of the following correctly states the hypotheses? O A. Ho: 01 72 Ha: 01 = 02 O B. Ho: 01 >02 Ha: 0102 Ha: 01 #02 O E. Ho: 01 =02 Ha: 01 02 nts SCO Compute the test statistic F. Scor (Round to three decimal places as needed.) ess
- An immunologist is testing the hypothesis that the current flu vaccine is less than 71% effective against the flu virus. The immunologist is using a 10% significance level and thesehypotheses: H0: p=0.71 and Ha: p<0.71. Explain what the 10% significance level means in context.A personnel director in a particular state claims that the mean annual income is greater in one of the state's counties (county A) than it is in another county (county B). In County A, a random sample of 6 residents has a mean annual income of $41,400 and a standard deviation of $8400. In County B, a random sample of 8 residents has a mean annual income of $39,800 and a standard deviation of $5200. At a = 0.10, answer parts (a) through (e). Assume the population variances are not equal. If convenient, use technology to solve the problem. (a) Identify the claim and state Ho and Ha. Which is the correct claim below? A. "The mean annual income in county A is less than in county B." B. "The mean annual incomes in counties A and B are not equal." C. "The mean annual incomes in counties A and B are equal." D. "The mean annual income in county A is greater than in county B." What are H, and Ha? The null hypothesis, Ho, is The alternative hypothesis, Ha, is Which hypothesis is the claim? The…A new reading program may reduce the number of elementary school students who read below grade level. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 8,400 children in several different school districts. Statistical analysis of the results showed that the percentage of students who did not meet the grade-level goal was reduced from 14.7% to 14%. The hypothesis that the new reading program produced no improvement was rejected with a P-value of 0.026. Complete parts a) and b) below. a) Explain what the P-value means in this context. Choose the correct answer below. OA. There is a 97.4% chance of seeing a sample proportion of 14.7% (or more) of students failing the test by natural sampling variation if 14% is the true population value. B. There is only a 2.6% chance of seeing a sample proportion of 14.7% (or more) of students failing the test by natural sampling variation if 14% is the true population value. OC. There…
