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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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Give all your answers correct to two decimal places.

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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}}\\).

", "

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}}\\).

", "

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}}\\).

", "

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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