You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 31.6 47.4 70.6 107.4 53.9 86.3 70.6 86.3 61.7 46 74.4
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A: Introduction: Denote μ as the true mean.
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You wish to test the claim μ≠81.6μ≠81.6 at a significance level of 0.0010.001.
You believe the population is
| data |
|---|
| 31.6 |
| 47.4 |
| 70.6 |
| 107.4 |
| 53.9 |
| 86.3 |
| 70.6 |
| 86.3 |
| 61.7 |
| 46 |
| 74.4 |
What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
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- You wish to test the following claim (H.) at a significance level of a = 0.002. H.:µ = 55.7 На:и < 55.7 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 24.5 35.2 1.8 10 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... O less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null hypothesis accept the null hypothesis fail to reject the null hypothesis As such, the final conclusion is that... O There is enough evidence to show that the population mean is not less than 55.7. There is not enough evidence to show that the population mean is not less than 55.7. OThere is enough evidence to show that the population mean is less than 55.7. There is not enough evidence to show that the…Suppose that you expect college freshmen who live on campus will do better academically than those who do not. You select a random sample of 75 freshmen, group them according to where they live, and calculate the following summary statistics. Do these results support your expectations? Assume that the true population standard deviations are equal. Use α = 0.10. Use α = 0.05. What is the p-value of this test?You wish to test the following claim (Ha) at a significance level of a = 0.02. H.:µ = 90.2 Ha:u + 90.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 80.7 89.4 86.3 86.1 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 =
- You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ=86.2 Ha:μ<86.2You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 64.7 65.6 80.7 58.2 71.3 97.6 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... The sample data support the claim that the population mean is less than 86.2. There is not sufficient sample evidence to support the claim that the population mean is less than 86.2. Next Next QuestionYou wish to test the following claim (Ha) at a significance level of a = 0.05. Ho:μ = 79.2 79.2 Ha: You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 25 with mean M = 75.4 and a standard deviation of SD = 8.7. 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... O less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.2. O The sample data support the claim that the population mean is…You wish to test the following claim (H) at a significance level of a = 0.05. H.:µ = 65.2 Ha:µ < 65.2 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 571 with mean M = 63.2 and a standard deviation of SD = 20.3. 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) a O greater than a 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. O There is sufficient evidence to warrant rejection of the claim that the population mean is less than 65.2. O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 65.2. O The sample data support the claim that the population mean is less than 65.2.…
- You wish to test the following claim (Ha) at a significance level of a = 0.01. Ho: H 63.6 На: и > 63.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 66.9 78.6 53.8 57.9 57 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 =What is the test statistic and P value?You wish to test the following claim (Ha) at a significance level of a = 0.01. H.:µ = 73.7 HaiH + 73.7 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 54 mean: M = 65.8 standard deviation: SD = 20.1. What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P-value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... less than (or equal to) a greater than a This leads to a decision to... reject the null accept the null fail to reject the null So, the final conclusion is that... The data do not support the claim of the alternative hypothesis that the population mean is not equal to 73.7. The sample data support the claim of the alternative hypothesis that the population mean is not equal to 73.7.
- You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:μ=66.4Ho:μ=66.4 Ha:μ>66.4Ha:μ>66.4You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 100.4 87.6 88.2 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? (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 greater than 66.4. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.4. The sample data support the claim that the…You wish to test the following claim (H.) at a significance level of a = 0.01. H.:µ = 75.8 Ha:µ > 75.8 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 73 mean: M = 77.2 standard deviation: SD = 8.5. What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P.value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... O less than (or equal to) a O greater than a This leads to a decision to... O reject the null O accept the null O fail to reject the null So, the final conclusion is that... O The data do not support the claim of the alternative hypothesis that the population mean is greater than 75.8. O The sample data support the claim of the alternative hypothesis that the population mean is greater than 75.8.For a sample, a score that is 12 points above the mean has a z-score of z = 1.20. What is the sample standard deviation?
