1. The sample mean weights for two varieties of lettuce grown for 16 days in a controlled environment are 3.259 and 1.413 and the corresponding sample standard deviations are .400 and .220. If the sample sizes for the two varieties are 9 and 6 respectively, what are the critical values for testing equality of mean weights ? A. 2.18 B. -2.18 and 2.18 C. -1.78 D. -1.78 and 1.78 2. What is your decision using critical value approach in problem 1? A. The computed test statistic falls in the critical region and we do not reject the null hypothesis. B. The computed test statistic does not fall in the critical region and we do not reject the null hypothesis. C. The computed test statistic falls in the critical region and we reject the null hypothesis. D. The computed test statistic does not fall in the critical region and we reject the null hypothesis. 3.What is the best conclusion based on problem 2? A. At 5% level, the two varieties of lettuce have exactly the same average weight. B. At 5% level, the two varieties of lettuce do not have significantly different average weight. C. At 5% level, the two varieties of lettuce have significantly different average weight. D. At 5% level, one variety of lettuce has significantly higher average weight.
1. The sample
Given mean sample weights of two varieties of lettuce
For lettuce-1
Mean = 3.259
Standard deviation = 0.4
Sample size = 9
For lettuce-2
Mean = 1.413
Standard deviation = 0.220
Sample size = 6
1)
Here two sample pooled t test is conducted to test for equality of mean weights.
Degree of freedom = 9 + 6 - 2 = 13
With reference to t table for 13 degree of freedom and 95% confidence interval critical values are -2.16 and 1.26
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