Answer:
Read it and do your best
Step-by-step explanation:
Part A:
Significant level:
<span>α = 0.05
Null and alternative hypothesis:
</span><span>h0 : μ = 3 vs h1: μ ≠ 3
Test statistics:
P-value:
P(-0.9467) = 0.1719
Since the test is a two-tailed test, p-value = 2(0.1719) = 0.3438
Conclusion:
Since the p-value is greater than the significant level, we fail to reject the null hypothesis and conclude that there is no sufficient evidence that the true mean is different from 3.
Part B:
The power of the test is given by:
Therefore, the power of the test if </span><span>μ = 3.25 is 0.8105.
Part C:
</span>The <span>sample size that would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9 is obtained as follows:
Therefore, the </span>s<span>ample size that would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9 is 16.</span>
The distance travelled by an object at time t is given by: d = stwhere d is the distance, s is the speed and t is the time.
Given that the cheetah travels a maximum of 70mph, the distance travelled by the cheetah travelling at 70mph at time t is given by d = 70t
There are 60 mins in one hour, so the distance given in miles per minutes is d = 70/60t = 1.167 miles per minutes.
Part B:
Given that t = 10 minutes, the distance covered by the cheetah in 10 minutes is d = 1.167 x 10 = 11.67 miles.
Part C:
If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the first 8 minutes is given by
d = 1.167 x 8 = 9.33 miles.
Part D:
If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the second 8 minutes is given by
d = 40/60 x 8 = 5.33 miles
Part E:
The distance the cheetah traveled in the first 8 minutes more than in the second 8 minutes is given by
9.33 miles - 5.33 miles = 4 miles.
Part F:
The ratio of the distance travelled in the first 8 minutes to the distance travelled in the next minutes is given by
9.33 : 5.33 = 1.75 : 1.
Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.