. XYZ has vertices X (–5, 2), Y (0, –4), and Z (3, 3). What are the vertices of the image of X’Y’Z’ under the translation (x, y)
1 answer:
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Answer:
The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.
Step-by-step explanation:
Test if the proportion is less than 40%:
At the null hypothesis, we test if the proportion is of at least 0.4, that is:
At the alternative hypothesis, we test if the proportion is of less than 0.4, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.4 is tested at the null hypothesis:
This means that
74 out of the 200 workers sampled said they would return to work
This means that
Value of the test statistic:
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.37, which is the p-value of z = -0.87.
Looking at the z-table, z = -0.87 has a p-value of 0.1922.
The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.
Answer:
Test statistic t=6.505
P-value=0
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that parents tend to underestimate their youngest child's size.
Then, the null and alternative hypothesis are:
The significance level is assumed to be 0.05.
The sample has a size n=39.
The sample mean is M=7.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.2.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a right-tailed test, with 38 degrees of freedom and t=6.505, so the P-value for this test is calculated as (using a t-table):
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that parents tend to underestimate their youngest child's size.