2. [6] Below is data from a sample of elected presidents and their main opponent in the same year. Is there sufficient evidence (at a = 0.05) to show that president elects are taller than the losing candidate? Height (cm) of President Height (cm) of Opponent 189 173 183 180 179 184 184 180 180 175 180 179 180 181 Show rejection regions with labelled critical value(s) Но: Hi: Critical Value(s): Test Statistic: [Must state what test stat is being used (z, t, etc.) the formula being used, and what values are substituted into the formula for full credit. Simply writing a number will not earn credit]
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- 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.A study carried out to investigate the distribution of totalbraking time (reaction time plus accelerator-to-brake movementtime, in ms) during real driving conditions at 60 km/hr gave the following summary information on the distributionof times (“A Field Study on Braking ResponsesDuring Driving,” Ergonomics, 1995: 1903–1910):mean 5 535 median 5 500 mode 5 500sd 5 96 minimum 5 220 maximum 5 9255th percentile 5 400 10th percentile 5 43090th percentile 5 640 95th percentile 5 720What can you conclude about the shape of a histogramof this data? Explain your reasoning.Suppose a statistician named Big Daddy thinks that the average monthly electric bill for Houston in August is more than $150. Using sample data from a normal population, Big Daddy obtains a test statistic of z = 1.06. Determine the P-value and state the conclusion at the 5% level of significance.
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- 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.)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?
- A major credit card company is interested in the proportion of individuals who use a competitor’s credit card. Their null hypothesis is H0: p=0.65H0: p=0.65, and based on a sample they find a sample proportion of 0.70 and a pp-value of 0.053. Is there convincing statistical evidence at the 0.05 level of significance that the true proportion of individuals who use the competitor’s card is actually greater than 0.65 ?You are conducting a study to determine if there is a significant difference between average adult weight of males and females (in pounds). Calculate the test-statistic, t with the following sample data.n1=25n1=25, ¯x1=153x¯1=153, s1=3s1=3n2=60n2=60, ¯x2=156x¯2=156, s2=3s2=3Rounded to 2 decimal places.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. a. 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. b. If the sample had n = 25 participants, is the correlation significant? Again, use a two-tailed test with α = .05. In your response, be sure to specify the critical value for r.