[ \( 1 / 8 \) Points] Classes SIS K-12 360 Launch DETAILS MY NOTES BBUNDERSTAT12HS 8.4.013. PREVIOUS ANSWERS ASK YOUR TEACHER In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's \( t \) table, use the closest \( d . f \). that is smaller. In some situations, this choice of \( d . f \). may increase the \( P \)-value by a small amount and therefore produce a slightly more "conservative" answer. In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the U.S. and foreign countries. Sex ratios for eight study sites in northern Europe are shown below. \begin{tabular}{|lcc|} \hline Location of Wolf Pack & \( \% \) Males (Winter) & \( \% \) Males (Summer) \\ \hline Finland & 90 & 47 \\ Finland & 82 & 69 \\ Finland & 60 & 63 \\ Lapland & 55 & 48 \\ Lapland & 64 & 55 \\ Russia & 50 & 50 \\ Russia & 41 & 50 \\ Russia & 55 & 45 \\ \hline \end{tabular} It is hypothesized that in winter, "loner" males (not present in summer packs) join the pack to increase survival rate. Use a \( 5 \% \) level of significance to test the claim that the average percentage of males in a wolf pack is higher in winter. (Let \( d= \) winter - summer.) (a) What is the level of significance? \[ 0.05 \] State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? \( H_{0}: \mu_{d}>0 ; H_{1}: \mu_{d}=0 \); right-tailed \( H_{0}: \mu_{d}=0 ; H_{1}: \mu_{d}>0 \); right-tailed \( H_{0}: \mu_{d}=0 ; H_{1}: \mu_{d}<0 \); left-tailed
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The level of significance for this hypothesis test is given as 0.05. This means that there is a 5% risk of concluding that a difference exists when there is actually no difference. Show more…
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Please provide the following information for Problems $11-22$. (a) What is the level of significance? State the null and alternate hypotheses. (b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution 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. Note: For degrees of freedom $d . f .$ not given in the Student's $t$ table, use the closest $d . f .$ that is smaller. In some situations, this choice of $d . f .$ may increase the $P$ -value by a small amount and therefore produce a slightly more "conservative" answer. Wildlife: Coyotes A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be $\bar{x}=2.05$ years, with sample standard deviation $s=0.82$ years (based on information from the book Coyotes: Biology, Behavior and Management by M. Bekoff, Academic Press). However, it is thought that the overall population mean age of coyotes is $\mu=1.75$. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of $1.75$ years? Use $\alpha=0.01$
Hypothesis Testing
Testing the Mean $\mu$
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data: B: Percent increase for company 14 16 12 18 6 4 21 37 A: Percent increase for CEO 19 26 16 14 -4 19 15 30 Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. Solve the problem using the critical region method of testing. (Let d = B − A. Round your answers to three decimal places.) test statistic = critical value = ± In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Wilderness District 1 2 3 4 5 January 129 131 126 64 78 April 113 95 106 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use 𝛼 = 0.01. Solve the problem using the critical region method of testing. (Let d = January − April. Round your answers to three decimal places.) test statistic = critical value =
Sri K.
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail. An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 15 7 11 10 13 21 13 9 6 10 23 21 13 7 10 5 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and ̃ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use ̑ = 0.01. (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? H0: ̐ = 11%; H1: ̐ > 11%; right-tailed H0: ̐ ≠ 11%; H1: ̐ = 11%; two-tailed H0: ̐ = 11%; H1: ̐ ≠ 11%; two-tailed H0: ̐ = 11%; H1: ̐ < 11%; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since we assume that x has a normal distribution with known ̓. The standard normal, since we assume that x has a normal distribution with unknown ̓. The standard normal, since we assume that x has a normal distribution with known ̓. The Student's t, since n is large with unknown ̓. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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