Find the critical välue(s) and rejection region(s) for the indicated t-test, level of significance a, and sample size n. Left-tailed test, a = 0.01, n= 14
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- Zachary works as a quality control engineer at Ford Motor Company. One of his job responsibilities is estimating the proportion of defective engines coming off a production line. The production line setting allows for a defective rate of 5%. In a periodical quality checkup, Zachary selected 100 engines that came off the production line. What is the chance Zachary will find more than 10 defective engines? The corresponding Z score is _____The average retirement age in America is 63 years old. Do small business owners retire at a different average age? The data below shows the results of a survey of small business owners who have recently retired. Assume that the distribution of the population is normal. 66, 60, 62, 71, 58, 73, 60, 72, 70, 61, 57 What can be concluded at the the a 0.05 level of significance level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: uv = 63 H: uv> c. The test statistic ? = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? a f. Based on this, we should Select an answerv the null hypothesis. g. Thus, the final conclusion is that O The data suggest the population mean retirement age for small business owners is not significantly different from 63 at a = 0.05, so there is insufficient evidence to conclude that the population mean…Phyllodes tumors of the breast are rare tumors that represent less than one percent of growths in the breast. Some researchers presented characteristics of phyllodes tumors in an article. The following table provides summary statistics for the sizes, in millimeters (mm) of independent samples of benign and malignant phyllodes tumors. Suppose that these tumor sizes are normally distributed. Use the nonpooled t-test to answer the following: At the 1% significance level, do the data provide sufficient evidence to conclude that, on average, malignant phyllodes tumors are larger than benign phyllodes tumors? a. Hypotheses: H0: ___________________ Ha: __________________________ b. Compute the test statistic: c. Determine the p-value. d. Reject null? e. Step 6: Interpret your result in a sentence
- Nutrition Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 56 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.40 mg with standard deviation 4.71 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.41 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. You can use the Inferential Statistics page and the Distribution Calculators page in SALT to answer parts of this question. (a) State the hypotheses (in mg) that we can use to consider this question. (Enter != for as needed.) Ho: H₁: (b) Carry out the hypothesis test in part (a) using the critical-value method with an a level of 0.05, and summarize your findings. Find the test statistic. (Round your answer to two decimal places.) Find the…The critical value in a hypothesis test Multiple Choice depends on the value of the test statistic. is calculated from the sample data. separates the acceptance and rejection regions. usually is .05 or .01 in most statistical tests.Perform a hypothesis test to determine whether there is a difference in the mean attendance of teams between the two groups created in Part F. Use a 0.05 level of significance in your testing procedures. Hint: When calculating your pooled sample variance and your test statistic, assume the Top 10 data is sample 1 and the Bottom 10 data is sample 2. Decision Rule -t < or t > = REJECT H0 Value of Pooled Sample Variances Value of test statistic Decision: enter Reject or Do Not Reject Is there a difference in the mean attendance between the two groups assuming a 0.05 level of significance? Enter Yes or No. Another variable that can impact attendance is the team's win-loss record. Teams that are winning more games are thought to have increased attendance as fans prefer to see their home team "win" rather than "lose" (although for some teams such as the Chicago Cubs, this is not always an established relationship!). Create 2 samples…
- Nutrition Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 53 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.60 mg with standard deviation 4.73 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.48 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. You can use the Inferential Statistics page and the Distribution Calculators page SALT to answer parts of this question. (a) State the hypotheses (in mg) that we can use to consider this question. (Enter != for + as needed.) Ho: Hi: (b) Carry out the hypothesis test in part (a) using the critical-value method with an a level of 0.05, and summarize your findings. Find the test statistic. (Round your answer to two decimal places.) Find the…Using the t-table, find the critical value for a left-tailed test with a significance level of 10% and a sample size of 25.To determine diet quality, male weanling rats were fed diets with various protein levels. Each of 15 rats was randomly assigned to one of three diets, and their weight gain in grams was recorded in the following table: Diet protein level Medium Low High 9.72 8.54 9.19 9.67 9.32 11.11 8.15 8.76 14.45 6.75 9.30 10.39 9.55 10.45 12.16 Sample Mean Sample Variance 1.696 8.768 9.274 11.460 0.547 3.963 Suppose we fit the data with the following model: Xij = µ+a; + Eij, i = 1, 2, 3; j= 1,., 5, N(0, o²) independently. Define X;. i = 1,2, 3, X. = 1=1 Xij, and SS(E) = E-1E=1(Xij – X;.)². E- Xij for where a1 + a2 + az = 0 and Eij Some R output that may help. > p1 qf (p1, 2, 12) [1] 0.010 0.025 0.052 0.106 2.807 3.885 5.096 6.927 > qf (p1, 2, 14) [1] 0.010 0.025 0.051 O.106 2.726 3.739 4.857 6.515 > qf (p1, 3, 12) [1] 0.037 0.070 0.114 O.192 2.606 3.490 4.474 5.953 > qf (p1, 3, 14) [1] 0.037 0.070 0.115 0.192 2.522 3.344 4.242 5.564