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Caiden K

Caiden K.

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The following problem is based on information taken from Academe, Bulletin of the American Association of University Professors. Let $x$ represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of $x$ is approximately $\sigma^{2}=47.1 .$ However, a random sample of 15 colleges and universities in Kansas showed that $x$ has a sample variance $s^{2}=83.2 .$ Use a $5 \%$ level of significance to test the claim that the variance for colleges and universities in Kansas is greater than $47.1 .$ Find a $95 \%$ confidence interval for the population variance.

The following problem is based on information taken from Academe, Bulletin of the American Association of University Professors. Let $x$ represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of $x$ is approximately $\sigma^{2}=47.1 .$ However, a random sample of 15 colleges and universities in Kansas showed that $x$ has a sample variance $s^{2}=83.2 .$ Use a $5 \%$ level of significance to test the claim that the variance for colleges and universities in Kansas is greater than $47.1 .$ Find a $95 \%$ confidence interval for the population variance.

Understandable Statistics, Concepts and Methods

Chi-Square and F Distributions

Testing and Estimating a Single Variance…
Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution? (c) Find or estimate the $P$ -value of the sample test statistic. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? (e) Interpret your conclusion in the context of the application. (f) Find the requested confidence interval for the population variance or population standard deviation. Interpret the results in the context of the application. Professors: Salaries The following problem is based on information taken from Academe, Bulletin of the American Association of University Professors. Let $x$ represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of $x$ is approximately $\sigma^{2}=47.1$. However, a random sample of 15 colleges and universities in Kansas showed that $x$ has a sample variance $s^{2}=83.2 .$ Use a $5 \%$ level of significance to test the claim that the variance for colleges and universities in Kansas is greater than $47.1$. Find a $95 \%$ confidence interval for the population variance.

Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution? (c) Find or estimate the $P$ -value of the sample test statistic. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? (e) Interpret your conclusion in the context of the application. (f) Find the requested confidence interval for the population variance or population standard deviation. Interpret the results in the context of the application. Professors: Salaries The following problem is based on information taken from Academe, Bulletin of the American Association of University Professors. Let $x$ represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of $x$ is approximately $\sigma^{2}=47.1$. However, a random sample of 15 colleges and universities in Kansas showed that $x$ has a sample variance $s^{2}=83.2 .$ Use a $5 \%$ level of significance to test the claim that the variance for colleges and universities in Kansas is greater than $47.1$. Find a $95 \%$ confidence interval for the population variance.

Understandable Statistics Concepts and Methods

Chi-Square and $F$ Distributions

Testing and Estimating a Single Variance…

Questions asked

ANSWERED

Hoan Nguyen verified

Numerade educator

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z β‰₯ 1.34) = Shade the corresponding area under the standard normal curve.

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Hoan Nguyen verified

Numerade educator

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ≀ βˆ’0.23) = Shade the corresponding area under the standard normal curve.

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Hoan Nguyen verified

Numerade educator

A normal distribution has ? = 34 and ? = 5. (a) Find the z score corresponding to x = 29. (b) Find the z score corresponding to x = 46. (c) Find the raw score corresponding to z = βˆ’3. (d) Find the raw score corresponding to z = 1.3.

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Given that x is a normal variable with mean ? = 51 and standard deviation ? = 7.1, find the following probabilities. (Round your answers to four decimal places.) (a) P(x ≀ 60) (b) P(x β‰₯ 50) (c) P(50 ≀ x ≀ 60)

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Jacob Mclean verified

Numerade educator

The average annual miles driven per vehicle in the United States is 11.1 thousand miles, with 𝜎 β‰ˆ 600 miles. Suppose that a random sample of 41 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.9 thousand miles. Does this indicate that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average? Use a 0.05 level of significance. State the null and alternate hypotheses. H0: p = 11.1; H1: p < 11.1 H0: p = 11.1; H1: p β‰  11.1 H0: p = 11.1; H1: p > 11.1 H0: πœ‡ = 11.1; H1: πœ‡ β‰  11.1 H0: πœ‡ = 11.1; H1: πœ‡ < 11.1 H0: πœ‡ = 11.1; H1: πœ‡ > 11.1 c) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010

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ANSWERED

Qudsiya Anis verified

Numerade educator

The average annual miles driven per vehicle in the United States is 11.1 thousand miles, with 𝜎 β‰ˆ 600 miles. Suppose that a random sample of 41 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.9 thousand miles. Does this indicate that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average? Use a 0.05 level of significance. a)State the null and alternate hypotheses. b)What sampling distribution will you use? What assumptions are you making? c)Find (or estimate) the P-value.

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ANSWERED

Kari Hasz verified

Numerade educator

The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the time of replacement were (in months): 34 36 47 48 53 46 30 51 42 52 (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 ?? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the injection system lasts less than an average of 48 months. There is insufficient evidence at the 0.05 level to conclude that the injection system lasts less than an average of 48 months.

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ANSWERED

Kari Hasz verified

Numerade educator

A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of 86 urban residents showed that 14 subscribed, and a random sample of 96 suburban residents showed that 20 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 10% level of significance. What is the value of the sample test statistic? (Test the difference p1 βˆ’ p2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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