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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

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

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

Given a sample of size \\(n\\) recall:

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

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

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}\\)

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

significance 10% 5% 1%

limits \\(\\pm1.65\\) \\(\\pm1.96\\) \\(\\pm2.58\\)

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

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The resting heart rate of 30 Irish women, selected at random, were measured and recorded in beats per minute. The data collected is presented below.

\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[23]}

{r1[24]}

{r1[25]}

{r1[26]}

{r1[27]}

{r1[28]}

{r1[29]}

It is believed that the mean heart rate for Irish women is \\(\\simplify{{mu1}-{k}}\\) beats per minute.

Does the data support this theory?

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

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

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

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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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Reject the Null Hypothesis and conclude that mean resting heart rate for an Irish woman is not \\(\\simplify{{mu1}-{k}}\\) beats per minute.

", "

Reject the Null Hypothesis at the 5% significance level but accept the Null Hypothesis at the 1% significance level and conclude that mean resting heart rate for an Irish woman is \\(\\simplify{{mu1}-{k}}\\) beats per minute.

", "

Reject the Null Hypothesis at the 10% significance level but accept the Null Hypothesis at the 5% significance level and conclude that mean resting heart rate for an Irish woman is \\(\\simplify{{mu1}-{k}}\\) beats per minute.

", "

Accept the Null Hypothesis at the 10% significance level and conclude that mean resting heart rate for an Irish woman is \\(\\simplify{{mu1}-{k}}\\) beats per minute.

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