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Ber [7]
3 years ago
11

In recent years the mean number of miles driven per year by residents of a particular state was 11,568. A researcher wishes to t

est, at the 5% level of significance, whether the mean is different now. In a random sample of 62 drivers, the mean and sample standard deviation of the number of miles driven last year were 10,822 and 1,741, respectively. The rejection region for the relevant test is:
Mathematics
1 answer:
aleksandrvk [35]3 years ago
8 0

Answer:

The degrees of freedom are given by:

df =n-1= 62 -1=61

And we want to find a critical value on the t distribution with 61 degrees of freedom who accumulates 0.025 of the area on each tail and the critical value would be t_{\alpha/2}= \pm 2.00

And the rejection region would be |t_{calc}| >2.00

Step-by-step explanation:

Data given and notation  

\bar X=10822 represent the sample mean  

s=1741 represent the sample standard deviation

n=62 sample size  

\mu_o =11568 represent the value that we want to test  

\alpha=0.05 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean differs from 11568, the system of hypothesis would be:  

Null hypothesis:\mu =11568  

Alternative hypothesis:\mu \neq 11568  

The degrees of freedom are given by:

df =n-1= 62 -1=61

And we want to find a critical value on the t distribution with 61 degrees of freedom who accumulates 0.025 of the area on each tail and the critical value would be t_{\alpha/2}= \pm 2.00

And the rejection region would be |t_{calc}| >2.00

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