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Two samples are shown in Table 10.2. Both have normal distributions. The means for the two populations are thought to be the same. Is there a difference in the means? Test at the 5% level of significance.
Sample |
Sample Standard Deviation | ||
Population A | 25 | 5 | 1 |
Population B | 16 | 4.7 | 1.2 |
Table 10.2
NOTE When the sum of the sample sizes is larger than 30 (
Whether any difference in the means of the given two samples.
Answer to Problem 10.1TI
There is no sufficient evidence to conclude that the means of the two populations are not the same.
Explanation of Solution
Given information:
The given table shows two samples:
Sample size | Sample mean | Sample standard deviation | |
Population A | 25 | 5 | 1 |
Population B | 16 | 4.7 | 1.2 |
Both have normal distribution. The means of the two populations are thought to be same. Test at the 5% level of significance.
Solution:
The null hypothesis is
The alternative hypothesis is:
The significant level,
The p-value is 0.4125, which is much higher than 0.05, so we decline to reject the null hypothesis.
Hence, there is no sufficient evidence to conclude that the means of the two populations are not the same.
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