# College math questions and answers

Recent questions in Post Secondary

### A normal population has mean $$\displaystyle\mu={20}$$ and standard deviation $$\displaystyle\sigma={4}$$. What proportion of the population is less than 18?

Efan Halliday 2020-10-25 Answered

### A population of values has a normal distribution with $$\displaystyle\mu={239.5}$$ and $$\displaystyle\sigma={32.7}$$. You intend to draw a random sample of size $$\displaystyle{n}={139}$$. Find the probability that a sample of size $$n=139$$ is randomly selected with a mean greater than 235.9. $$\displaystyle{P}{\left({M}{>}{235.9}\right)}=$$? Write your answers as numbers accurate to 4 decimal places.

Dolly Robinson 2020-10-25 Answered

### Solve. $$\displaystyle\int\frac{{\sqrt{{x}}}}{{{1}+{\sqrt[{{3}}]{{x}}}}}{\left.{d}{x}\right.}=?$$

Isa Trevino 2020-10-23 Answered

### Let F be a field. Prove that there are infinitely many irreducible monic polynomials

Mylo O'Moore 2020-10-23 Answered

### Write down a definition of a subfield. Prove that the intersection of a set of subfields of a field F is again a field

Jaya Legge 2020-10-23 Answered

### A random sample of $$\displaystyle{n}_{{1}}={16}$$ communities in western Kansas gave the following information for people under 25 years of age. $$\displaystyle{X}_{{1}}:$$ Rate of hay fever per 1000 population for people under 25 $$\begin{array}{|c|c|} \hline 97 & 91 & 121 & 129 & 94 & 123 & 112 &93\\ \hline 125 & 95 & 125 & 117 & 97 & 122 & 127 & 88 \\ \hline \end{array}$$ A random sample of $$\displaystyle{n}_{{2}}={14}$$ regions in western Kansas gave the following information for people over 50 years old. $$\displaystyle{X}_{{2}}:$$ Rate of hay fever per 1000 population for people over 50 $$\begin{array}{|c|c|} \hline 94 & 109 & 99 & 95 & 113 & 88 & 110\\ \hline 79 & 115 & 100 & 89 & 114 & 85 & 96\\ \hline \end{array}$$ (i) Use a calculator to calculate $$\displaystyle\overline{{x}}_{{1}},{s}_{{1}},\overline{{x}}_{{2}},{\quad\text{and}\quad}{s}_{{2}}.$$ (Round your answers to two decimal places.) (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 $$\displaystyle\alpha={0.05}.$$ (a) What is the level of significance? State the null and alternate hypotheses. $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}<\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}>\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}\ne\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}>\mu_{{2}},{H}_{{1}}:\mu_{{1}}=\mu_{{12}}$$ (b) What sampling distribution will you use? What assumptions are you making? 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, The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations, The Student's t. We assume that both population distributions are approximately normal with known standard deviations, What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimalplaces.) What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value $$\displaystyle>{0.250}$$ $$\displaystyle{0.125}<{P}-\text{value}<{0},{250}$$ $$\displaystyle{0},{050}<{P}-\text{value}<{0},{125}$$ $$\displaystyle{0},{025}<{P}-\text{value}<{0},{050}$$ $$\displaystyle{0},{005}<{P}-\text{value}<{0},{025}$$ P-value $$\displaystyle<{0.005}$$ Sketch the sampling distribution and show the area corresponding to the P-value. P.vaiue Pevgiue P-value f P-value

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