Question

An agricultural researcher is studying the effectiveness of a pesticide named Malathion in reducing cereal leaf beetle damage to oat plants. In his study, he measured the number of beetle larvae per stem in two randomly selected one acre plots of oats after applying Malathion to one of the plots (and applying no pesticide to the other plot). From the one acre plot in which no pesticide was applied, he took 53 sample measurements and determined that the mean number of larvae per stem was 7.67 with a standard deviation of 1.21. From the one acre plot in which Malathion was applied, he took 54 sample measurements and determined that the mean number of larvae per stem was 7.11 with a standard deviation of 0.52. The standard error (SE) of the difference between the sample means is 0.181. a) Would you consider the difference in sample means to be practically significant? Why or why not? Briefly discuss the difference between statistical significance and practical significance in your response. b) Using SE = 0.181, is there sufficient evidence, at the 5% significance level, to conclude that the mean number of beetle larvae per stem is lower for oat plants treated with Malathion than for untreated oat plants? Show your work. Conduct a complete analysis and state your conclusion in the context of the researcher’s study. (continued) c) Based on your conclusion, what type of error (Type 1 or Type 2) is possible? Why? Explain what that type of error would mean in the context of this study

Answer 1

a) Would you consider the difference in sample means to be practically significant? Why or why not? Briefly discuss the difference between statistical significance and practical significance in your response.

While statistical significance relates to whether an effect exists, practical significance refers to the magnitude of the effect. However, no statistical test can tell you whether the effect is large enough to be important in your field of study.

b) Using SE = 0.181, is there sufficient evidence, at the 5% significance level, to conclude that the mean number of beetle larvae per stem is lower for oat plants treated with Malathion than for untreated oat plants? Show your work. Conduct a complete analysis and state your conclusion in the context of the researcher’s study. (continued)

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 > µ2

1	2
7.67	7.11	mean
1.21	0.52	std. dev.
53	54	n
	70	df
	0.56000	difference (1 - 2)
	0.18064	standard error of difference
	0	hypothesized difference
	3.100	t
	.0014	p-value (one-tailed, upper)

The p-value is 0.0014.

Since the p-value (0.0014) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the mean number of beetle larvae per stem is lower for oat plants treated with Malathion than for untreated oat plants.

c) Based on your conclusion, what type of error (Type 1 or Type 2) is possible? Why? Explain what that type of error would mean in the context of this study

Type I error could be made because we reject the null hypothesis.

This means that we concluded the mean number of beetle larvae per stem is lower for oat plants treated with Malathion than for untreated oat plants when it is not true.

Please give me a thumbs-up if this helps you out. Thank you!