91Ó°ÊÓ

Population $1:$ Fraud offences, ${\stackrel{¯}{x}}_1=10.12,s_1=4.90$, and $n_1=10$.

Population 2 : Firearms offences, ${\stackrel{¯}{x}}_2=18.78,s_1=4.64$, and $n_2=10$.

Significance level is $5\%$.

A statement is expressed as - for a left-tailed hypothesis test.

The null hypothesis $H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2$will be rejected in favour of the alternate hypothesis $H_a:{\mathrm{μ}}_1<{\mathrm{μ}}_2$at the significance level $\mathrm{Î\pm }$if and only if the $(1-\mathrm{Î\pm })$-level upper confidence bound for ${\mathrm{μ}}_1-{\mathrm{μ}}_2$is less than or equal to $0$.

The test statistic falls in the rejection zone of the left-tailed hypotheses test starting with exercise $10.45$and a significance level of $5\%$. As a result, null hypotheses are ruled out.

The $95\%$confidence interval for exercise $10.51$is $-12.36$to $-4.96$.

Population $1$: Male, ${\stackrel{¯}{x}}_1=37.6,s_1=38.5$and $n_1=30$.

Population $2$ : Female, ${\stackrel{¯}{x}}_2=55.8,s_2=48.3$, and $n_2=30$.

Significance level is $5\%$.

A statement is supplied as for a left-tailed hypothesis test. A statement is given as - for a left-tailed-hypothesis test.

If and only if the $(1-\mathrm{Î\pm })$-level upper confidence bound for ${\mathrm{μ}}_1-{\mathrm{μ}}_2$is less than or equal to $0$, the null hypothesis $H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2$will be rejected in favour of the alternate hypothesis $H_a:{\mathrm{μ}}_1<{\mathrm{μ}}_2$at the significance level $\mathrm{Î\pm }$.

The test statistic for exercise $10.46$does not fall inside the rejection region of the left-tailed hypotheses test at a significance level of $5\%$. Null hypotheses are therefore not rejected.

The $95$percent confidence interval from exercise $10.52$to $8.84$is $-45.24$to $-45.24$.