What is 7/8 times 3/4
2 answers:
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Answer:
a. P-value = 0.039.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the population mean significantly differs from 100.
b. P-value = 0.013.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the population mean significantly differs from 100.
c. P-value = 0.130.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the population mean significantly differs from 100.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean significantly differs from 100.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=65.
The degrees of freedom for this sample size are:
a. The sample mean is M=103.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.5.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
This test is a two-tailed test, with 64 degrees of freedom and t=2.103, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.039) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the population mean significantly differs from 100.
b. The sample mean is M=96.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
This test is a two-tailed test, with 64 degrees of freedom and t=-2.565, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.013) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the population mean significantly differs from 100.
c. The sample mean is M=102.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=10.5.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
This test is a two-tailed test, with 64 degrees of freedom and t=1.536, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.13) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the population mean significantly differs from 100.
Check the picture below.
ok, notice the volume of the smaller cube forming the larger cube. Keeping in mind that the larger cube has 90 of those small ones.
ok, notice the volume of the smaller cube forming the larger cube. Keeping in mind that the larger cube has 90 of those small ones.