You wish to test the following claim (H1H1) at a significance level of α=0.005.
Ho:μ1=μ2
H1:μ1≠μ2
You believe both populations are
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The p-value is...
- less than (or equal to) αα
- greater than αα
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 warrant rejection of the claim that the first population mean is not equal to the second population mean.
- There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.
- The sample data support the claim that the first population mean is not equal to the second population mean.
- There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.
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- It is desired to test Ho: 50 against Ho: 50, using a sample size of n = 13 from a normal population with mean and variance ². Suppose that the true mean is = 50 +0.75 a Which one of the following statements is incorrect? O a. O b. O C. O d. O a. O b. O c Hypotheses: Ho: μ = 50 against Ho:μ + 50. In a random sample of 36 observations from a bivariate normal distribution, it was found that the sample correlation coefficient r = 0.4. If we want to test the significance of the correlation at the 5% level of significance, which one of the following statements is incorrect? O d. The probability of type 2 error at the 5% level of significance is 0.69. The probability of type I error at the 5% level significance is 0.31. The power of the test at the 5% level of significance is 0.35. Ho: p=0 against Ho: p0. T = 2.5448. The critical value is 2.032. We do not reject H, at the 5% level of significance. Let Y, and Y₂ be independent random variables such that E(Y₂) 0₁ E(₂) 0₂ and VAR(Y) =VAR(₂)= ².…arrow_forwardYou wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:μ=51.3Ho:μ=51.3 Ha:μ≠51.3Ha:μ≠51.3You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=12n=12 with mean M=49.2M=49.2 and a standard deviation of SD=5.5SD=5.5.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = CorrectWhat is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = Incorrect0.2128 or 0.2127The p-value is... less than (or equal to) αα greater than αα Correct This test statistic leads to a decision to... reject the null accept the null fail to reject the null Correct As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 51.3. There is not sufficient evidence to warrant rejection of the claim that the population mean is…arrow_forwardIn a test of hypothesis, the null hypothesis is that the population mean is less than or equal to 32 and the alternative hypothesis is that the population mean is greater than 32. The population has a normal distribution with variance of 12.5. The test is to be made at the 10% significance level. A sample of size 41 is selected from this population. The approximate value of ßatu = 32. 35 is a. 0.5403 O d. 0.7414 O e. 0.9000 O b. 0.2586 O c. 0.9723arrow_forward
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- You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:μ=58.8Ho:μ=58.8 Ha:μ>58.8Ha:μ>58.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=298n=298 with mean M=59.6M=59.6 and a standard deviation of SD=7.3SD=7.3.What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =arrow_forwardYou wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:μ=81.6Ho:μ=81.6 Ha:μ<81.6Ha:μ<81.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=638n=638 with mean M=81M=81 and a standard deviation of SD=11.3SD=11.3.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα 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 warrant rejection of the claim that the population mean is less than 81.6. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 81.6. The sample data support the…arrow_forwardLet x represent the number of mountain climbers killed each year. The long-term variance of x is approximately σ2 = 136.2. Suppose that for the past 11 years, the variance has been s2 = 111.3. Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2. Find a 90% confidence interval for the population variance. (a) What is the level of significance? (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? (c)Find the requested confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limitarrow_forward
- You wish to test the following claim (H1H1) at a significance level of α=0.10α=0.10. Ho:μ=66.8Ho:μ=66.8 H1:μ>66.8H1:μ>66.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 44.5 103.2 74.3 72.1 50.6 63.6 52.2 68.5 29.6 What is the critical value for this test? (Report answer accurate to four decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to four decimal places.) test statistic = The test statistic is... in the critical region not in the critical region 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 warrant rejection of the claim that the population mean is greater than 66.8. There is not sufficient evidence to warrant rejection of the claim that the population mean…arrow_forwardYou wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1>μ2Ha:μ1>μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain the following two samples of data. Sample #1 Sample #2 69 85.7 80.8 85.7 85.1 83.8 85.7 77.7 68.4 73 64.1 52.4 97.5 76.3 79.8 84.2 90.2 72.5 60.6 70 75.4 38.6 72.9 96.4 83.1 57 104.3 34 60.6 46.9 69.1 63.2 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic…arrow_forwardYou wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:μ=52.2Ho:μ=52.2 Ha:μ<52.2Ha:μ<52.2You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 50.3 38.5 38.2 56.1 44.2 47.1 What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα 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 warrant rejection of the claim that the population mean is less than 52.2. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 52.2. The sample data support the…arrow_forward
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