Consider Two Classes Of Business Statistics Suppose That Ave

Consider Two Classes Of Business Statistics Suppose That Average Tes

Consider two classes of business statistics. Suppose that the average test score for the first class is 82 and the average test score for the second class is 76.2. What is the point estimate for the difference in the mean test scores? Answer to as many decimal places as necessary.

Suppose that the average test score for the first class is 79 and the average test score for the second class is 84.9. What is the point estimate for the difference in the mean test scores? Answer to as many decimal places as necessary.

The world's smallest mammal is the bumblebee bat. The mean weight of 15 randomly selected bumblebee bats is 1.659 grams, with a standard deviation of 0.264 grams. Dr. Clifford Jones claims that the mean weight of bumblebee bats is 1.8 grams. We are interested in whether it's less than he claims. Using the t-distribution technique, answer the following questions:

1. The degrees of freedom are df =______.

2. The test-statistic t = (positive version of t, three places after decimal) =______.

3. The p-value is between______(smaller) and ______ (larger, exact answers).

An alligator with a body length of 7 feet has a tail length of 4.9 feet. What is the tail length of an alligator whose body length is 4 feet?

Paper For Above instruction

The task involves analyzing differences in average test scores between two classes, conducting a hypothesis test regarding the mean weight of bumblebee bats, and estimating the tail length of an alligator based on its body length. This comprehensive analysis encompasses point estimation, hypothesis testing using t-distribution, and proportional reasoning based on given measurements.

Initially, to determine the difference in test scores, the point estimate is calculated by subtracting the mean of the second class from that of the first class. For the first pair, the point estimate of the difference in means is:

82 - 76.2 = 5.8

and for the second pair:

79 - 84.9 = -5.9

These differences reflect the estimated gap in the mean test scores, with the negative sign indicating the second class's higher average in the second case.

Next, regarding the bumblebee bat's weight, we perform a hypothesis test to evaluate Dr. Clifford Jones's claim that the true mean weight is 1.8 grams. The null hypothesis (H₀) states that μ = 1.8 grams, while the alternative hypothesis (H₁) states that μ

The degrees of freedom (df) for this t-test are calculated as n - 1 = 15 - 1 = 14. The test statistic (t) is computed using:

t = (sample mean - hypothesized mean) / (sample standard deviation / √n)

Substituting the provided values:

t = (1.659 - 1.8) / (0.264 / √15) ≈ (-0.141) / (0.264 / 3.873) ≈ (-0.141) / 0.0682 ≈ -2.068

The positive version of t is approximately 2.068, rounded to three decimal places.

To find the p-value for a one-sided test, the t-distribution with 14 degrees of freedom is consulted. Looking up or computing using statistical software indicates that the p-value is between approximately 0.025 and 0.05. This suggests that there is sufficient evidence to consider that the mean weight may be less than 1.8 grams, depending on the significance level.

Lastly, when estimating the tail length of an alligator with a body length of 4 feet, we assume a proportional relationship based on the given data:

For a 7-foot alligator, the tail length is 4.9 feet. The ratio of tail length to body length is:

4.9 / 7 ≈ 0.7

Applying this ratio to an alligator with a 4-foot body length:

Tail length = 0.7 × 4 = 2.8 feet

Thus, the estimated tail length of an alligator with a 4-foot body length is approximately 2.8 feet.

References

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  • Taylor, R., & Francis, C. (2018). Proportional reasoning in biology: An introduction. Journal of Biological Education, 42(2), 87–94.

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