Question

In a sample survey, six estimates were made of the same mean. When the population mean became known, the following errors were computed: -35, 111, -88, 47, -12, 26. are these errors consistent with the hypothesis that the population of errors has a zero mean?

Answer 1

Answer on Question #76159 – Math – Statistics and Probability

Question

In a sample survey, six estimates were made of the same mean. When the population mean became known, the following errors were computed: -35, 111, -88, 47, -12, 26. are these errors consistent with the hypothesis that the population of errors has a zero mean?

Solution

$$\bar{x} = \frac{1}{6} \sum_{i=1}^{6} x_i = 8.17.$$ $$s = \sqrt{\frac{1}{5} \sum_{i=1}^{6} (x_i - \bar{x})^2} = 69.16$$

Null hypothesis $H_0$: $\mu = 0$.

Alternative hypothesis $H_a$: $\mu \neq 0$.

Test statistic: $t = \frac{\bar{x} - \mu}{s / \sqrt{n}} = \frac{8.17 - 0}{\frac{69.16}{\sqrt{6}}} = 0.29$.

P-value: $p = 0.7835$.

Since the P-value is greater than 0.05 we fail to reject the null hypothesis and should conclude that these errors consistent with the hypothesis that the population of errors has a zero mean.

**Answer**: These errors consistent with the hypothesis that the population of errors has a zero mean.

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