Question

soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the

wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds).

4.02 3.75 4.14 4.11 3.93 3.79 4.09 4.42 3.89 3.87 4.12 3.09 4.86 2.90 5.01 3.39

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.301.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

3.43 3.43 3.55 3.79 3.94 3.72 4.13 4.01 3.59 4.29 3.78 3.19 3.84 3.91 3.66 4.35

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.100.

Test the claim that the population variance of annual wheat production for the first plot is larger than that for the second plot. Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²    H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

df_N

df_D

What assumptions are you making about the original distribution?

The populations follow dependent normal distributions. We have random samples from each population. The populations follow independent normal distributions.    The populations follow independent normal distributions. We have random samples from each population. The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.100 0.050 < p-value < 0.100    0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production is greater in the first plot. Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production is greater in the first plot.    Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production is greater in the first plot. Fail to reject the null hypothe

 

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Question

Do larger universities tend to have more property crime? University crime statistics are affected by a variety of

factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.

x 13.7, 29.4, 24.5, 14.3, 7.5, 27.7, 16.2, 20.1

y 23, 76, 39, 23, 15, 30, 15, 25

(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 153.4, Σx² = 3346.78, Σy = 246, Σy² = 10330 and Σxy = 5522.9.

*** Compute r. (Round to 3 decimal places.)

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

i.  Given our value of r, y should tend to decrease as x increases.

ii.  Given our value of r, y should tend to increase as x increases.    

iii. Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

iv.  Given our value of r, y should tend to remain constant as x increases.

 

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