State the null and alternative hypotheses to determine if the average number of hours until spoilage begins differs for the preservatives A and B. Assume population variances are equal. Calculate the pooled variance and the value of the test statistic. t: Determine the rejection region at a = .05 and write the proper conclusion. Rejection region: Decision: Conclusion:
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It is given that
For preservative A, sample size n1 = 16, sample mean = 108.7 and sample SD s1 = 10.5
For preservative B, sample size n2 = 16, sample mean = 98.7 ans sample SD s2 = 13.6
Level of significance = 0.05
Step by step
Solved in 4 steps with 2 images
- 11. Hypothesis Test of Equal Variances. Test the given claim. Use a significance level of a = 0.05 and assume that all populations are normally distributed. Claim: The treatment population and the placebo population have different variances. n = 16, x = 21.33, s = 0.80 n = 41, x = 25.34, s = 0.40 Treatment group : Placebo group :Do Predicted Temperatures match Actual Temperatures? The table shows the predicted and actual temperatures for a seven day period. Assume that the two samples are randomly selected. At the 0.1 significance level, test the claim that there is no mean difference in the predicted and actual temperatures.(Be sure to subtract in the same direction). Predicted Temperatures ⁰F Actual Temperatures ⁰F Difference ⁰F 81 76 75 79 86 83 85 90 82 82 77 78 78 80 What are the correct hypotheses? (Select the correct symbols and values.)H0: Select an answer p μ₁ s₁² μ(d) σ₁² x̄₂ μ x̄₁ ? < = > ≥ ≠ ≤ Select an answer s₁² μ 0 σ₁² μ₂ μ₁ x̄₁ p x̄₂ H1: Select an answer μ₂ x̄₁ x̄₂ p μ s₂² μ₁ μ(d) σ₂² ? ≤ ≠ > ≥ < = Select an answer μ₂ x̄₂ μ 0 σ₁² x̄₁ μ₁ p s₁² Original Claim = Select an answer H₁ H₀ df = Based on the hypotheses, find the following: Test Statistic = (Round to three decimal places.)Critical value(s) = ±± (Round to three decimal…1
- Treatment Placebo 3. H1 H2 table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. A study was done using a treatment group and a placebo group. The results are shown in the 27 40 In 2.39 2.65 0.95 0.57 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? O A. Ho: H1 = H2 O B. Ho: H1H2 D. Ho: H1 H2 The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. O A. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. O B. Reject the null hypothesis. There is not sufficient evidence to warrant rejection…A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Treatment Placebo μ μ1 μ2 n 26 32 x 2.38 2.63 s 0.85 0.57 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? A. H0: μ1<μ2 H1: μ1≥μ2 B. H0: μ1=μ2 H1: μ1≠μ2 Your answer is correct. C. H0: μ1=μ2 H1: μ1>μ2 D. H0: μ1≠μ2 H1: μ1<μ2 The test statistic, t, is negative 1.28−1.28. (Round to two decimal places as needed.) The P-value is 0.2060.206. (Round to three decimal places as needed.) State the conclusion for the test. A.…Is there a difference between the ages of Actors and Actresses? The table shows the ages of Actors and Actress when they received their first Oscar. Assume that the two samples are randomly selected. At the 0.1 significance level, test the claim that there is a mean difference in the ages of Actors and Actresses. (Be sure to subtract in the same direction). Actor (years) Actress (years) Difference (years) 60 60 52 56 61 61 62 58 36 36 49 51 45 50 What are the correct hypotheses? (Select the correct symbols and values.) Họ: Select an answer ? v Select an answer H1: Select an answer v ? v Select an answer Original Claim = Select an answer df = 15
- Two-Sample T-Test for Mean A researcher wants to study the effect of bold and underlined words on students. A group of 20 students received a syllabus with the academic integrity section in bold and underlined words while another group of 20 students received the same copy except everything was in normal font. For the group with the bold and underlined words, the mean number of students who violated the academic integrity policy was 1.5 with a sample variance of 0.85. For the group with the normal font, the mean number of students who violated the academic integrity policy was 2.3 with a sample variance of 1.22. Do the results indicate a significantly higher mean number of students who violated the academic integrity policy for the normal font group? Use a 5% significance level. Please use ALL the four steps of hypothesis testing to answer this question.The accompanying data table lists the magnitudes of 50 earthquakes measured on the Richter scale. Test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a 0.01 significance level. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and conclusion for the test. Assume this is a simple random sample.Incorrect An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.6 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 120 engines and the mean pressure was 6.8 pounds/square inch. Assume the variance is known to be 1.00. A level of significance of 0.05 will be used. Determine the decision rule. Enter the decision rule. Answer E Tables E Keypad How to enter your answer Keyboard Shortcuts Reject Ho if z> Tutor Skip Try Similar Submit Ansgr O 2020 Hawkes Learning MacBook Air 888 esc F1 #3 %23 & + 1 5 8 delete Q W R T Y U tab A S D G H K return caps lock C V B N M shift shift control option command command option
- 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 sentenceA study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random. samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H1 H2 H₁₁₂ The test statistic, t, is (Round to two decimal places as needed.) OB. Ho: H₁₂ H₁: H₁SEE MORE QUESTIONS