91Ó°ÊÓ

Check whether the data provide sufficient evidence to conclude that on average the angle between the body and head of an alligator during a death roll is greater than ${45}^{°}$

State the null and alternative hypothesis:

Null Hypothesis:

${\mathrm{H}}_0:\mathrm{μ}={45}^{°}$

That is, the data does not provide sufficient evidence to conclude that on average the angle between the body and head of an alligator during a death roll is greater than ${45}^{°}$

Alternative Hypothesis:

$H_a:\mathrm{μ}>45°$

That is, the data provide sufficient evidence to conclude that on average the angle between the body and head of an alligator during a death roll is greater than $45°$

Decide a significance level

Here, the significance level is, $\mathrm{Î\pm }=0.05$

Compute the value of test statistic and P value using MINITAB

MINITAB procedure:

Step 1: Choose Stat > Basic Statistics > 1-Sample t.

Step 2: In Summarized data, enter the sample size 20 and mean 49 .

Step 3: In Standard deviation, enter a value 10 .

Step 4: InPerform hypothesis test, enter the test mean as 45.

Step 5: Check Options, enter Confidence levelas 95 .

Step 6: Choose greater thanin alternative.

Step 7: Click OK in all dialogue boxes.

MINITAB output:

One-Sample T

Test of mu = 45 vs $>$45

From the MINITAB Output the value of test statistic is localid="1651581810106" $\boxed{1.79}$

From the MINITB Output, The P-value is localid="1651581819598" $\boxed{0.045}$

Conclusion

If $\mathrm{P}≤\mathrm{Î\pm }$, then reject the null hypothesis.

Here the P-Value is 0.045 which is less than the level of significance. That is,

$P\left(=0.045\right)<\mathrm{Î\pm }\left(=0.05\right)$

Therefore, the null hypothesis is rejected at $5\%$level.

Thus, it can be conclude that the test results are statistically significant at $5\%$level of significance.

Interpretation:

Thus, the data provide sufficient evidence to conclude that on average the angle between the body and head of an alligator during a death roll is greater than $45°$.