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The null hypothesis is μ≥700 and alternative hypothesis is μ<700, the type of test statistic is t statistic, the statistical test value is -2.650, the critical value is -1.796 and the null hypothesis is reject.
Given the average monthly rent for apartments on the east side of the cities is $700, and the mean for a random sample of 12-month rents for apartments on the east side is $687, with a standard deviation of $17.
Statistical hypothesis testing is an important technique in inferential statistics. Used to test hypotheses about population parameters. Statistical tests are used to compute test statistics and p-values. Finally, use this test statistic and the p-value to make a decision about rejecting the null hypothesis.
(a) Let μ be the population and monthly rent. the null and alternative hypotheses are given below.
Null Hypothesis: μ≥700
Alternative hypothesis: μ< 700 This is a left-sided hypothesis test.
(b) Here, the sample size is less than 30 and the population mean is unknown. Therefore, a one-sample t-test can be used here. Therefore, the t statistic is the test statistic.
(c) Given [tex]\bar{x}[/tex]=687, s=17 and n=12, the test statistic is computed as
[tex]\begin{aligned}t&=\frac{\bar{x}-\mu_{0}}{s/\sqrt{n}}\\ &=\frac{687-700}{17/\sqrt{12}}\\ &=-2.64901888216\\ &=-2.650\end[/tex]
(d) For n-1=12-1=11 degrees of freedom
The critical value for a significance level of 0.05 with 11 degrees of freedom is
[tex]\begin{aligned}t_{crit}&=-1.7959\\ &=-1.796\end[/tex]
(e) Reject the null hypothesis because the statistical test value (-2.650) is less than the critical value (-1.796). There is ample evidence to support the claim that the average monthly rent for East Side apartments is lower than stated on the website.
Hence, The value of test statistic and critical value has a mean of $687 and a standard deviation of $17, which are -2.650 and -1.796.
Learn more about test statistic from here brainly.com/question/16194574
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