PLEASEEEEEE HELP ME OUT

If we compare the p value and a significance level for example $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean it's not significantly less than 20 min.

Step-by-step explanation:

Data given and notation

$\bar X=18.81$ represent the average lateral recumbency for the sample

$s=8.4$ represent the sample standard deviation

$n=75$ sample size

$\mu_o =20$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t 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 apply a left tailed test.

What are H0 and Ha for this study?

Null hypothesis: $\mu \geq 20$

Alternative hypothesis : $\mu < 20$

Compute the test statistic

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

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

$t=\frac{18.81-20}{\frac{8.4}{\sqrt{75}}}=-1.227$

The degrees of freedom are given by:

$df=n-1=75-1=74$

Give the appropriate conclusion for the test

Since is a one side left tailed test the p value would be:

$p_v =P(t_{74}$

Conclusion

If we compare the p value and a significance level for example $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean it's not significantly less than 20 min.

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3 years ago