Dave likes to grow cucumbers, and each year he experiments with ways to improve his crop. This summer, he wants to determine whether the new fertilizer he has seen advertised will increase the mean number of cucumbers produced per plant. He uses the old fertilizer on 15 cucumber plants and the new fertilizer on the other 13 plants. Over the course of the growing season, he calculates a mean of 17.4 cucumbers per plant for the old fertilizer, with a standard deviation of 2.0 cucumbers. He calculates a mean of 21.6 cucumbers per plant for the new fertilizer, with a standard deviation of 2.7 cucumbers. You may assume that both samples came from populations that are approximately normal. Assume that the population variances are not equal. a. Determine the best point estimate for the true mean difference in cucumber production. Correct notation counts. b. Construct a 95% confidence interval for the true mean difference in cucumber production. For credit, your work must include a filled-out formula for your confidence interval. State your interval using interval notation. c. Interpret the confidence interval in the context of the original problem
13. Dave likes to grow cucumbers, and each year he experiments with ways to improve his crop. This summer, he wants to determine whether the new fertilizer he has seen advertised will increase the mean number of cucumbers produced per plant. He uses the old fertilizer on 15 cucumber plants and the new fertilizer on the other 13 plants. Over the course of the growing season, he calculates a mean of 17.4 cucumbers per plant for the old fertilizer, with a standard deviation of 2.0 cucumbers. He calculates a mean of 21.6 cucumbers per plant for the new fertilizer, with a standard deviation of 2.7 cucumbers. You may assume that both samples came from populations that are approximately normal. Assume that the population variances are not equal.
a. Determine the best point estimate for the true mean difference in cucumber production. Correct notation counts.
b. Construct a 95% confidence interval for the true mean difference in cucumber production. For credit, your work must include a filled-out formula for your confidence interval. State your interval using interval notation.
c. Interpret the confidence interval in the context of the original problem.
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