Which of the following best describes the slope of the line below?

When we compare the significance level $\alpha=0.1$ we see that $p_v$ so we can reject the null hypothesis at 10% of significance. So the the true mean is difference from 21 at this significance level.

Step-by-step explanation:

Data given and notation

$\bar X=23$ represent the sample mean

$\sigma=3.5$ represent the population standard deviation

$n=49$ sample size

$\mu_o =21$ represent the value that we want to test

$\alpha=0.1$ 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 average age of the evening students is significantly different from 21, the system of hypothesis would be:

Null hypothesis: $\mu = 21$

Alternative hypothesis: $\mu \neq 21$

The statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{23-21}{\frac{3.5}{\sqrt{49}}}=4$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(z>4)=0.0000633$

Conclusion

When we compare the significance level $\alpha=0.1$ we see that $p_v$ so we can reject the null hypothesis at 10% of significance. So the the true mean is difference from 21 at this significance level.

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3 years ago