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In this example we have a single sample of 30 data values. The sample is just large enough to apply a Z-test

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\$$H_0:\$$ The mean \$$=\\simplify{{mu1}-{k}}\$$.

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\$$H_1:\$$ The mean \$$\\ne \\simplify{{mu1}-{k}}\$$.

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Given a sample of size \$$n\$$ recall:

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the formula for the sample mean:    \$$\\overline{x}=\\frac{\\sum {x}}{n}=\\var{sample_mean_2}\$$

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the formula for the sample standard deviation:   \$$s=\\sqrt{\\frac{\\sum{(x-\\overline{x})^2}}{n-1}}=\\var{sample_stdev_2}\$$

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the formula for the Z-statistic:   \$$Z=\\frac{\\overline{x}-\\mu}{\\frac{s}{\\sqrt{n}}}=\\frac{\\var{sample_mean_2}-\\simplify{{mu1}-{k}}}{\\frac{\\var{sample_stdev_2}}{\\sqrt{\\var{sample_size}}}}=\\var{test_statistic}\$$

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The Z-table values will be for a two-tailed test are given below.

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significance              10%                    5%                   1%

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limits                \$$\\pm1.65\$$             \$$\\pm1.96\$$             \$$\\pm2.58\$$

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Compare the test statistic with the Z-table values and choose your conclusion.

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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 {r1[0]} {r1[1]} {r1[2]} {r1[3]} {r1[4]} {r1[5]} {r1[6]} {r1[7]} {r1[8]} {r1[9]} {r1[10]} {r1[11]} {r1[12]} {r1[13]} {r1[14]} {r1[15]} {r1[16]} {r1[17]} {r1[18]} {r1[19]} {r1[20]} {r1[21]} {r1[22]} {r1[29]} {r1[23]} {r1[24]} {r1[25]} {r1[26]} {r1[27]} {r1[28]}
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It is believed that the mean lifespan for Irish men is \$$\\simplify{{mu1}-{k}}\$$ years.

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Does the data support this theory?

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Input the sample mean:   \$$\\bar{x}=\$$ [[0]]

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Input the sample standard deviation:   \$$s=\$$ [[1]]

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Enter the value for the test statistic:   \$$Z=\$$ [[2]]

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Reject the Null Hypothesis and conclude that mean lifespan for an Irish man is not \$$\\simplify{{mu1}-{k}}\$$.

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Reject the Null Hypothesis at the 5% significance level but accept the Null Hypothesis at the 1% significance level and conclude that mean lifespan for an Irish man is \$$\\simplify{{mu1}-{k}}\$$.

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Reject the Null Hypothesis at the 10% significance level but accept the Null Hypothesis at the 5% significance level and conclude that mean lifespan for an Irish man is \$$\\simplify{{mu1}-{k}}\$$.

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Accept the Null Hypothesis at the 10% significance level and conclude that meanlifespan for an Irish man is \$$\\simplify{{mu1}-{k}}\$$.

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Having compared your test statistic with the table values for a two-tailed Z-test, select one of the following conclusions that best describes your conclusion.

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