91影视

given,

Assume that the population standard deviation of the lengths of imprisonment for motor-vehicle-theft offenders in Sydney is 6.0 months.

Given that,

Population standard deviation is,

$蟽=6.8$years

Now, test the hypotheses,

$\begin{array}{r}{H}_0:渭=72\text{b.p.m}\\ H_a:渭>72\text{b.p.m}\end{array}$

Perform the test at a $5\%$level of significance i.e., $伪=0.05$

The sample size was $n=29$

The sample mean is,

$\overline{x}=78.3bpm$

$\begin{array}{r}\text{Test statistic,}z=\frac{\stackrel{炉}{x}鈭�{渭}_0}{\frac{蟽}{\sqrt{n}}}\\ =\frac{78.3鈭�72}{\frac{11.2}{\sqrt{29}}}\\ =3.03\end{array}$

Since the test is left the tailed test with $伪=0.05$,

and the critical value is,

localid="1651233032648" $z_{伪}=z_{0.05}=1.645$

Here, the region is,

$z>z_{0.05}$

i.e., $z>1.645$

$z=3.03>z_{0.05}=1.645$

Since $z$ does not fall in the rejection region.

Thus, $H_0$is not rejected at a $5\%$level of significance of the test value statistic.

At the $1\%$significance level, the data provided is sufficient evidence for concluding that the mean post-work heart rate for easting workers exceeds the normal resting heart rate of $72bpm$.