A quarter cone has a diameter of 16 and a height of 10. What is the approximate volume of the quarter cone? Round to the nearest
1 answer:
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Regarding the hypothesis tested in this problem, it is found that:
a) The test statistic is: t = 0.49.
b) The p-value is: 0.6297..
c) The null hypothesis is not rejected, as the p-value is greater than the significance level.
d) It appears that the students are legitimately good at estimating one minute, as the sample does not give enough evidence to reject the null hypothesis.
<h3>What is the test statistic?</h3>The test statistic of the t-distribution is given by the equation presented as follows:
In which the variables of the equation are given as follows:
is the sample mean.
is the value tested at the hypotheses.
- s is the standard deviation of the sample.
- n is the sample size.
The value tested at the hypothesis is:
From the sample, using a calculator, the other parameters are given as follows:
Hence the test statistic is obtained as follows:
t = 0.49.
<h3>What are the p-value and the conclusion?</h3>The p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, in this case 60, with:
- 15 - 1 = 14 df, as the number of degrees of freedom is one less than the sample size.
- t = 0.49, as obtained above.
Hence the p-value is of 0.6297.
Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected, attesting to the ability of the students to estimate one minute.
More can be learned about the test of an hypothesis at brainly.com/question/13873630
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Answer:
7.5 hours
Step-by-step explanation:
Using the variable 't' for time, you can set up an equation to find out how long it will take the truck to catch up to the bus. Since the bus is traveling at 60mph and the truck is traveling 1 2/3 times faster, we need to first find the rate of the truck:
1
Using 't' and the knowledge that they will have traveled the same distance we the truck catches up to the bus and the fact that the truck left 3 hours later:
60t = 100(t - 3) or 60t = 100t - 300
Solve for 't': 60t - 100t = -300 or -40t = -300 so, t = 7.5 hours