A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. H0: μ ≥ 220 H1: μ < 220 (a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic.
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A sample of 64 observations is selected from a normal population. The sample
H0: μ ≥ 220
H1: μ < 220
(a) State the null hypothesis and the alternate hypothesis.
(b) State the decision rule.
(c) Compute the value of the test statistic.
(d) What is your decision regarding H0?
(e) What is the p-value? Interpret it.
Given that:
Sample size n =64
Sample mean is 215
Population Standard deviation is 15
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- You wish to test the following claim (H1) at a significance level of α=0.001. H0:μ=72.2 H1:μ≠72.2You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=7 with mean ¯x=58.1 and a standard deviation of s=14.9.What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = IncorrectWhat is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = IncorrectThe p-value is... less than (or equal to) α greater than α Correct This test statistic leads to a decision to... reject the null accept the null fail to reject the null Incorrect 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 72.2. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 72.2. The sample data support…You wish to test the following claim (Ha) at a significance level of α=0.02 Ho:μ=57.8 Ha:μ≠57.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=9with mean M=62.1 and a standard deviation of SD=11.6.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... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 57.8. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 57.8. The sample data support the claim that the population mean is not equal…You wish to test the following claim (Ha) at a significance level of a=0.02. H0: u=83.9 Ha:u<83.9 You believe the population is normally distributed but you do not know the standard deviation. You obtain a sample of size n=119 with the meanM=79.4 and a standard deviation of SD=12.9. What is the test statistic foe this sample? What is the P value for this sample? The p value is less than or greater than a? This test statistic leads to a decision to: reject the null, accept the null, or fail to reject the null?
- Jimmy collected a random sample of 30 psychology majors and administered an IQ test. This group had an average IQ of M = 110. Compare this statistic to the general population, which has a mean IQ of 100 and a standard deviation of 15. Use alpha of .05 and a two tailed test Step 1: Pick the Test: Hypotheses: Step 2: Alpha: One-tail or two-tail: Decision Rule (What is the critical value): Step 3: Calculations Step: 4 Interpretation What did you do? What did you find (include APA)? What does it mean? Did you reject or fail to reject null hypothesis: APA? Step 4:You wish to test the claim that the average IQ score is less than 100 at the .01 significance level. You determine the hypotheses are: Ho: μ=100 H1:μ<100H You take a simple random sample of 79 individuals and find the mean IQ score is 98.3, with a standard deviation of 15.3. Let's consider testing this hypothesis two ways: once with assuming the population standard deviation is not known and once with assuming that it is known. Round to three decimal places where appropriate. Assume Population Standard Deviation is NOT known Assume Population Standard Deviation is 15 Test Statistic: t = Test Statistic: z = Critical Value: t = Critical Value: z = p-value: p-value: Conclusion About the Null: Reject the null hypothesis Fail to reject the null hypothesis Conclusion About the Null: Reject the null hypothesis Fail to reject the null hypothesis Conclusion About the Claim: There is sufficient evidence to support the claim that the average IQ score is less…You wish to test the following claim (Ha) at a significance level of α=0.02. Ho:μ=63.3 Ha:μ>63.3You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=62 with mean M=68 and a standard deviation of SD=16.2.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) α greater than α 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 63.3. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 63.3. The sample data support the claim that the population mean is greater…
- Q1: A researcher was interested in the effect of exercise on stress levels. For the general population, the distribution of the Stress Battery Scale scores is normal with the mean of µ = 25 and the standard deviation of σ = 5. A sample of n = 100 participants was asked to exercise for three weeks and then reported their stress levels. The sample mean was ?X = 23. Conduct a hypothesis test and determine the effect of exercise. Use the two-tailed test α = .01 1.Type the null and research hypotheses in complete sentences. 2.Cut off points 3.Standard error and z-score -show your computation process 4.Your conclusion thoroughly.The manufacturer claims that your new car gets 24 mpg on the highway. You suspect that the mpg is less for your car. The 44 trips on the highway that you took averaged 22.3 mpg and the standard deviation for these 44 trips was 4.2 mpg. What can be concluded at the αα = 0.05 level of significance? For this study, we should use (t-test for population mean, z-test for population proportion) The null and alternative hypotheses would be: H0: (symbol) (symbol) ____ H1: (symbol) (symbol) ____ The test statistic (?,t,z) = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is (?, less than or equal to, more than) αα Based on this, we should (accept, reject, fail to reject) the null hypothesis. Thus, the final conclusion is that ... The data suggest that the sample mean is not significantly less than 24 at αα = 0.05, so there is statistically insignificant evidence to conclude…You wish to test the following claim (Ha) at a significance level of α=0.10 Ho:μ=73.8 Ha:μ<73.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=5 with a mean M=64.5 and a standard deviation of SD=10.9 What is the test statistic for this sample? (Report answers 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=81.9 Ha:μ≠81.9You 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=72.6M=72.6 and a standard deviation of SD=7.5SD=7.5.What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = ______The p-value is... A.) less than (or equal to) αα B.) greater than α This p-value leads to a decision to... A.) reject the null B.) accept the null C.) fail to reject the null As such, the final conclusion is that... A.) There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 81.9. B.) There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 81.9. C.) The sample data support the claim that the population mean is not equal to 81.9. D.) There is not sufficient sample evidence to…You wish to test the following claim (Ha) at a significance level of α=0.001. Ho:μ=66.6 Ha:μ≠66.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=24 with mean M=60 and a standard deviation of SD=14.7.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 which.... less than (or equal to) α greater than αThe manufacturer claims that your new car gets 23 mpg on the highway. You suspect that the mpg is less for your car. The 50 trips on the highway that you took averaged 19.8 mpg and the standard deviation for these 50 trips was 7.4 mpg. What can be concluded at the � = 0.10 level of significance? For this study, we should use The null and alternative hypotheses would be: �0: �1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is � Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest that the populaton mean is significantly less than 23 at � = 0.10, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is less than 23. The data suggest that the population mean is not significantly less than 23 at � = 0.10, so there is…
