MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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- In 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_forwardYou wish to test the following claim (H) at a significance level of a = 0.005. H₂:1 = μ₂ Ha: M1 M₂ You believe both populations are normally distributed, but you do not know the standard deviations for either. However, assume that the variances of the two populations are equal. You obtain a sample of size n₁ = 20 with a mean of ₁ = 60.9 and a standard deviation of SD₁ = 6.2 from the first population. You obtain a sample of size n₂ = 15 with a mean of 2 = 76.9 and a standard deviation of SD2 = 18.6 from the second population. 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 Ogreater than aarrow_forward15% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 322 people from the inner city surveyed, 42 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.01? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean The null and alternative hypotheses would be: Ho: ? p μ Select an answer > < = ≠ (please enter a decimal) H1: ? μ p Select an answer ≠ > = < (Please enter a decimal) 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 ? > ≤ αα Based on this, we should Select an answer reject accept fail to reject the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly smaller than 15% at αα = 0.01, so…arrow_forward
- The lowest level of significance to reject the null hypothesis of no linear association between blood pressure and age is: OA: 0.003 OB: 0.05 OC: 0.0002 OD: 0.0001 OE: 0.04arrow_forwardA claim is made that the proportion of children who play sports is less than it used to be. Assume that you plan to use a significance level of αα = 0.05 to test the claim that p<0.5p<0.5. Find the critical value for this hypothesis test, then use x=396x=396 and n=1320n=1320 from the sample data to decide if the statistics support the claim. -1.96; yes, they do support the claim -1.96; no, they do not support the claim -1.645; yes, they do support the claim -1.645; no, they do not support the claimarrow_forwardYou wish to test the following claim (Ha) at a significance level of α=0.01. Ho:μ1=μ2 Ha:μ1>μ2 You obtain a sample of size n1=13 with a mean of M1=65.1 and a standard deviation of SD1=15.8 from the first population. You obtain a sample of size n2=14 with a mean of M2=49.4 and a standard deviation of SD2=8.3 from the second population. Use the Theory-based inference applet to conduct the test of significance. (a) What is the t-score for this sample? t-score = (Round to 2 decimal places.) (b) What is the p-value for this sample? p-value = (Round to 4 decimal places.) (c) The p-value is... less than (or equal to) α greater than α (d) This p-value leads to a decision to... strong evidence in support of the alternative accept the null null is plausible (e) As such, the final conclusion is that... We conclude that μ1>μ2 . We conclude that μ1=μ2 . We have statistically significant evidence to support the claim that μ1>μ2 ..…arrow_forward
- You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test. Ho:μd=0Ho:μd=0 Ha:μd<0Ha:μd<0You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=12n=12 subjects. The average difference (post - pre) is ¯d=−44.4d¯=-44.4 with a standard deviation of the differences of sd=39.4sd=39.4.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 = 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…arrow_forwardA test of H₁: μ=7 versus H₁: u<7 is performed using a significance level of a=0.01. The P-value is 0.20. Part: 0/3 Part 1 of 3 (a) Is H rejected? Since P ≤ Part: 1 / 3 Part 2 of 3 (b) If the true value of u is 1, is the result a Type I error, a Type II error, or a correct decision? a, we do not reject Ho at the a= 0.01 level. The result is a Type I error Part: 2/3 Part 3 of 3 X 3 (c) If the true value of u is 7, is the result a Type I error, a Type II error, or a correct decision? The result is a [Choose one) ▾ Españolarrow_forwardTest the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .05 significance level.The null and alternative hypothesis would be: H0:μM=μFH1:μM<μF H0:pM=pFH1:pM<pF H0:pM=pFH1:pM>pF H0:pM=pFH1:pM≠pF H0:μM=μFH1:μM≠μF H0:μM=μFH1:μM>μF The test is: right-tailed left-tailed two-tailed Based on a sample of 20 men, 40% owned catsBased on a sample of 60 women, 55% owned catsThe test statistic is: (to 2 decimals)The p-value is: (to 2 decimals)Based on this we: Fail to reject the null hypothesis Reject the null hypothesisarrow_forward
- You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test. Ho:μd=0Ho:μd=0 Ha:μd>0Ha:μd>0You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=40n=40 subjects. The average difference (post - pre) is ¯d=3.2d¯=3.2 with a standard deviation of the differences of sd=9.6sd=9.6.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…arrow_forwardLet's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 by drawing samples from these values, calculating the mean of each sample, and then considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll an eight-sided die two times (or equivalently, roll two eight-sided dice one time) and calculate the mean of your sample. Remember that your population is the numbers 1, 2, 3, 4, 5, 6, 7, and 8. The true mean (p) of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 is The number of possible different samples (each of size n = 2) is the number of possibilities on the first roll (8) times the number of possibilities on the second roll (also 8), or 8(8) = 64. If you collected all of these possible samples, the mean of your sampling distribution of means (HM) would equal , and the standard deviation of your sampling distribution of means (that is, the standard error or GM) would be The following chart shows the sampling distribution of the…arrow_forwardTest the claim that the proportion of men who own cats is smaller than 90% at the .05 significance level.The null and alternative hypothesis would be: H0:μ=0.9H0:μ=0.9H1:μ>0.9H1:μ>0.9 H0:p=0.9H0:p=0.9H1:p>0.9H1:p>0.9 H0:p=0.9H0:p=0.9H1:p≠0.9H1:p≠0.9 H0:μ=0.9H0:μ=0.9H1:μ≠0.9H1:μ≠0.9 H0:μ=0.9H0:μ=0.9H1:μ<0.9H1:μ<0.9 H0:p=0.9H0:p=0.9H1:p<0.9H1:p<0.9 The test is: right-tailed two-tailed left-tailed Based on a sample of 65 people, 87% owned catsThe test statistic is: (to 2 decimals)The critical value is: (to 2 decimals)Based on this we: Fail to reject the null hypothesis Reject the null hypothesis I dont understand this.arrow_forward
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