A study was done to find the rate of hay fever in a population. A random sample of nā = 16 communities in western Kansas gave a sample mean of 109.50 and a sample standard deviation of 15.41 for people under 25 years of age. A random sample of nā = 14 communities in western Kansas gave a sample mean of 99.36 and a sample standard deviation of 11.57 for people over 50 years of age. Assume that the hay fever group has an approximately normal distribution. Does the data indicate that the age group over 50 has a different rate of hay fever? Use Ī± = 0.05. State the null and alternative hypothesis for this scenario. Find the level of significance. What assumptions have been met to ensure the tests are valid? Find the test statistic t. Find the p-value and determine what type of test (i.e. one-tail/two-tail) is being conducted. Highlight the correct decision by comparing the p-value with the level of significance. Reject Ho Fail to reject Ho Reject Ha Accept Ho Accept Ha Fail to reject Ha Interpret the results from part (f). Find the margin of error for a 95% confidence interval using the data. Create the 95% confidence interval and interpret the results.
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- Alternative Hypothesis (Ha): The mean hay fever rate for people under 25 years of age is not equal to the mean hay fever rate for people over 50 years of age. Show moreā¦
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A random sample of n1 = 16 communities in western Kansas gave the following rates of hay fever per 1000 population for people under 25 years of age: 121 115 124 99 134 121 110 116 113 96 116 116 135 96 96 116 A random sample of n2 = 14 communities in western Kansas gave the following rates of hay fever per 1000 population for people over 50 years old: 113 86 106 102 113 94 94 108 103 99 78 105 88 100 Assume that the hay fever rate in each age group has an approximately normal distribution. Using the method outlined in Brase and Brase, do the data indicate that the age group over 50 has a lower rate of hay fever? Use a significance level of 0.05. Do you reject or fail to reject the null hypothesis? Are the data statistically significant at the 0.05 level of significance? A. Since the p-value is greater than the level of significance, the data are not statistically significant. Thus, we fail to reject the null hypothesis. B. Since the p-value is less than the level of significance, the data are not statistically significant. Thus, we fail to reject the null hypothesis. C. Since the p-value is greater than the level of significance, the data are statistically significant. Thus, we fail to reject the null hypothesis. D. Since the p-value is less than the level of significance, the data are statistically significant. Thus, we reject the null hypothesis. E. Since the p-value is greater than the level of significance, the data are not statistically significant. Thus, we reject the null hypothesis.
Madhur L.
A random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age. x1: Rate of hay fever per 1000 population for people under 25 96 89 120 126 91 123 112 93 125 95 125 117 97 122 127 88 A random sample of n2 = 14 regions in western Kansas gave the following information for people over 50 years old. x2: Rate of hay fever per 1000 population for people over 50 97 110 103 96 113 88 110 79 115 100 89 114 85 96 (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use š¼ = 0.10. (a) What is the level of significance? State the null and alternate hypotheses. H0: š1 = š2; H1: š1 < š2H0: š1 > š2; H1: š1 = š2 H0: š1 = š2; H1: š1 ā š2H0: š1 = š2; H1: š1 > š (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference š1 ā š2. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the $z$ value of the sample test statistic. (c) Find (or estimate) the $P$ -value. Sketch the sampling distribution and show the area corresponding to the $P$ -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha ?$ (e) Interpret your conclusion in the context of the application. Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in $\mathrm{mg} / 100 \mathrm{ml}$ ). The sample mean is $\bar{x} \approx 93.8 .$ Let $x$ be a random variable representing glucose readings taken from Gentle Ben. We may assume that $x$ has a normal distribution, and we know from past experience that $\sigma=12.5 .$ The mean glucose level for horses should be $\mu=85 \mathrm{mg} / 100 \mathrm{ml}$ (Reference: Merck Veterinary Manual). Do these data indicate that Gentle Ben has an overall average glucose level higher than $85 ?$ Use $\alpha=0.05$
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