Carry out the hypothesis test for the mean of a normally distributed population given the following information: Ho: µ ≥2.5 Ha: µ ≠2.5 Sample size = 30 mean = 1.8, variance =1.7, α = .05
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A: As per guideline expert have to answer first 3 subparts only dear student please upload other parts…
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A: Given Null hypothesis:H0:μ=90.3 Alternative hypothesis:Ha:μ≠90.3 α=0.005 n=15 mean M=98.8 SD(S)=15.7
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A: n1=13, s12=59.5n2=21, s22=28.2
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A: n1 = 20n2 = 20x¯1 = 0.43x¯1 = 0.47s1 = 1.37s2 = 0.94 α = 0.05claim : σ12 > σ22
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Q: Carry out the hypothesis test for the mean of a normally distributed population given the following…
A: Given,H0:μ≥1.6Ha:μ≠1.6sample size(n)=15mean(x¯)=1.8standard deviation(s)=25=5α=0.10
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Q: (b) Find the critical value(s) assuming that the population variances are not equal.
A: (b) Degrees of freedom = min(n1-1, n2-1) = min(12-1, 10-1) = 9
Q: Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses,…
A: Sample sizes n1=6 n2=8
Carry out the hypothesis test for the
Ho: µ ≥2.5 Ha: µ ≠2.5
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- Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance a, and sample sizes n, and n2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). Ha H >H2; a = 0.05, n, = 14, n = 13 (a) Find the critical value(s) assuming that the population variances are equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)Consider the following two independently chosen samples whose population variances are not equal to each other. Sample 1 12.1 13.4 11.7 10.7 14.0 Sample 2 10.5 9.5 8.2 7.8 11.1 a) Using a significance level of 0.025, test the null hypothesis that µ1 - µ2 ≤ 0. b) Calculate the p-value.Given a result of t (30) = 1.55 for a one-tailed paired samples t-test, What is the sample size?
- Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance a, and sample sizes n, and n2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). %3D Ha: 12, a=0.02, n, = 15, n2 =8 (a) Find the critical value(s) assuming that the population variances are equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) (b) Find the critical value(s) assuming that the population variances are not equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) Next 2:15 PM 66°F Mostly cloudy ^ ED a 0 P Type here to search 11/22/2021 Inser 四 F6 PrtSc F3 F4 F5 F7 F8 F9 F10 F11 F12 F2 23 %24 & 3. 4 6. 7. 8 + II 团 5You 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…You 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…
- A) find the critical value(s) assuming that the population variances are equal . B) Find the critical value (s) assuming that they population variances are not equal.You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. 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. We will assume that the population variances are not equal. You obtain a sample of size n1=17 with a mean of M1=64.6 and a standard deviation of SD1=11.7 from the first population. You obtain a sample of size n2=17 with a mean of M2=53.2 and a standard deviation of SD2=8.9 from the second population.What is the test statistic for this sample? (Report answer accurate to three decimal places.)You wish to test the following claim (Ha) at a significance level of a 0.01. Ho: 41 Ha: µ1 # µ2 You 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 52.4 66.6 56.9 44 51.3 49.3 51.6 50.4 58.7 31.3 54.4 26.4 39.9 50.1 48.3 24.9 50.9 36.6 54.7 63.4 61.2 42.3 36.3 32.1 37.7 58.4 67.1 35.4 34.1 56.1 43.1 54.7 69 48 56.1 57.8 43.1 54.1 33.2 49.5 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 following data were obtained from an independent-measures study comparing three treatment conditions. Calculate the sample variance for each of the three samples. Use an ANOVA with α=.05 to determine whether there are any significant differences among the three treatment means.You wish to test the following claim (HaHa) at a significance level of α=0.05 Ho:μ1=μ2 Ha:μ1≠μ2You 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=23 with a mean of ¯x1=74.5 and a standard deviation of SD1=20.4 from the first population. You obtain a sample of size n2=11with a mean of ¯x2=89.8and a standard deviation of SD2=7.3 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... 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…You 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 obtain the following two samples of data. Sample #1 Sample #2 65.8 77.7 105.1 78.6 89.2 69.1 96.7 91.3 105.9 87.5 70.5 93.9 83.4 88.3 79.5 66.7 83.4 91.7 106.7 73 75.7 98.7 76.7 80 53.2 92.1 93 78.2 72.4 79.1 82.1 74.1 78.2 85.5 85.9 99.3 84.2 104.3 88.3 107.6 63.8 99.8 97.7 86.3 74.9 72.7 77.5 93.9 76.1 77.1 81.9 74.1 73.6 78.7 81.9 78.9 81.1 88 85.8 75.3 74.3 77.5 69.1 75.5 72.9 80.1 84.3 73.1 67.3 72.2 76.1 67.8 74.9 67.3 74.7 70.1 65.4 76.9 83.8 79.7 72.9 81.7 74.1 68.2 65.4 80.9 69.4 79.5 96 77.5 77.1 75.9 68.7 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? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four…
