Question

The heights of six randomly chosen sailors are, in inches, 63, 65, 58, 69, 71 and 72. The heights of 10 randomly chosen soldiers are, in inches, 61, 62, 65, 66, 69, 69, 70, 71, 72 and 73. Do these figures indicate that soldiers are on an average shorter than sailors? Test at 5% level of significance.

Answer 1

Answer:

No, this figure do not indicate that soldiers are on an average shorter than sailors.

Step-by-step explanation:

The t-statistic for difference of mean is given by,

$t=\frac{\bar{x_{1}}-\bar{x_{2}}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}$

Here $\bar{x_{1}}$ is the mean of sailors height

$\bar{x_{2}}$ is the mean of soldiers height

${s_{1}}^2$ is the variance of sailors height

${s_{2}}^2$ is the variance of soldiers height

Using this formula, we get, t = -0.61671

Thus, p-value = 0.273662 with 14 degree of freedom.

and α = 0.05

The result is not significant at p < .05.

Since, the p-value is greater than alpha (p > .05), then we fail to reject the null hypothesis, and we say  that the result is statistically non-significant.

Answer 2

Step-by-step explanation:

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