Compare the 2 calculations above by means of a diagram
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3.1.1)Given
X=14.5%
SD=3.4%
N=25
90% CI for population mean is
- X.where Z=1.645 at 905 confidence
=14.5±1.645
=14.5±1.12
=(13.38%,15.62%)
We are 90% confident that the actual mean dividend yield lies between 13.38% and 15.62%.
3.1.2)
95% CI is
X±Z where Z
=14.5±1.96.
=14.5±1.33
=(13.17%,15.83%) is the 95% Confidence interval
Compare the 2 calculations above by means of a diagram
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- A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 105.6 90.9 91.2 96.9 96.5 91.3 100.1 105.5 99.6 107.7 103.3 92.4 Does this data suggest that the population mean reading under these conditions differ from 100? State the null and alternative hypotheses. Calculate, correct to 2 decimal places, the sample mean, x ; and the sample standard deviation, s. Evaluate the appropriate test statistic. Test these hypotheses at 05 level of significance.The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…In a comparison of two methods for the determination of chromium in rye grass, the following results were obtained: Method A, mean(mg/kg Cr)=1.48 Standard deviation(mg/kg Cr)=0.28 n= 6 Method B, mean (mg/kg Cr)=2.33 Standard deviation(mg/kg Cr)=0.31 n=10 Is the precision of these two methods significantly different? Do these two methods give results with means which differ significantly? a=0.05
- A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 105.6 90.9 91.2 96.9 96.5 91.3 100.1 105.5 99.6 107.7 103.3 92.4 Does this data suggest that the population mean reading under these conditions differ from 100? (a) State the null and alternative hypotheses. (b) Calculate, correct to 2 decimal places, (i) the sample mean, x ; and (ii) the sample standard deviation, s. (c) Evaluate the appropriate test statistic. (d) Test these hypotheses at 0.05 level of significance.Ex 6.14 modified as follows: In a random sample of 55 panels, the average failure time is 2.07 years and the standard deviation is 1.11 years. Find the 91.7% CI for the population mean failure timeThe null and alternate hypotheses are:H0: μ₁ = μ2H1: μ₁ ≠ μ2 A random sample of 10 observations from one population revealed a sample mean of 26 and a sample standard deviation of 5.0. A random sample of 8 observations from another population revealed a sample mean of 30 and a sample standard deviation of 6.0. The population standard deviations are unknown but assumed to be equal. At the 0.01 significance level, is there a difference between the population means?
- Serum nitrite concentrations (in μmol/L) were compared between a group of unmedicated HIV+ subjects (n =7) and a control group (n = 10). The HIV+ distribution is strongly skewed.a) Use a Wilcoxon-Mann-Whitney U test to determine if there is convincing evidence at α = 0.05 thatserum nitrite levels differ between the two populations. b) What would have been the U test p-value if researchers had instead hypothesized that serum nitriteconcentrations would tend to be larger in the HIV+ population? HIV+ Control 0.266 0.167 0.269 0.201 0.299 0.205 0.335 0.232 0.503 0.234 0.846 0.260 0.946 0.268 0.288 0.301 0.305Serum nitrite concentrations (in μmol/L) were compared between a group of unmedicated HIV+ subjects (n =7) and a control group (n = 10). The HIV+ distribution is strongly skewed. a) Use a Wilcoxon-Mann-Whitney U test to determine if there is convincing evidence at α = 0.05 thatserum nitrite levels differ between the two populations. b) What would have been the U test p-value if researchers had instead hypothesized that serum nitriteconcentrations would tend to be larger in the HIV+ population?Assume that you have a sample of n1=8, with the sample mean X1=46, and a sample standard deviation of S1=6, and you have an independent sample of n2=6 from another population with a sample mean of X2=37 and the sample standard deviation S2=5. Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that μ1>μ2? Determine the hypotheses. Choose the correct answer below. A. H0: μ1≤μ2 H1: μ1>μ2 Your answer is correct. B. H0: μ1>μ2 H1: μ1≤μ2 C. H0: μ1≠μ2 H1: μ1=μ2 D. H0: μ1=μ2 H1: μ1≠μ2 Find the test statistic. tSTAT=
- As we have noted in previous chapters, even a very small effect can be significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation (computed from the raw data) of r = 0.60 for a sample of n = 10 participants. (4 pts. total) Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with α = .05. In your response, be sure to specify the critical value for r.Assume that you have a sample of n1=7 , with the sample mean X1=44 , and a sample standard deviation of S1=6 , and you have an independent sample of n2=6 from another population with a sample mean of X2=32 and the sample standard deviation S2=5 . Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that μ1>μ2?Assume that you have a sample of n1=8, with the sample mean X1=44, and a sample standard deviation of S1=5, and you have an independent sample of n2=14 from another population with a sample mean of X2=30 and the sample standard deviation S2=6. Using a significance level of α=0.025, what is the critical value for a one-tail test of the hypothesis H0: μ1≤ μ2 against the alternative H1: μ1>μ2? The critical value is ______ (Round to two decimal places as needed.)
