height shoe size (if you wear men's shoes, add 2)
61 6.5
67 9
63 7
66 8
60 6
71 10
71 11
63 8
63 7
66
62 7
64 6.5
61 7
64 7.5
63 8
58 6.5
63 9
62 6
61 7
74
60 6.5
60 7.5
63 8
Mean 63.73913043 7.571428571
Standard Deviation 3.922167667 1.296974501
H sub 0: x̄ = 8
H sub a: x̄ > 8
find critical value, test value
Im trying to figure this out but im having a hard time. I need to do a write-up. If someone can explain how the answer came about ..
Is that tabel two or one. You can make it clear.
Table two or one
Two table or one table
Some of the numbers are missing there.
To find the critical value and test value for the hypothesis test mentioned above, we need the sample mean and standard deviation.
Given the sample mean (x̄) and standard deviation for the shoe sizes:
Sample mean (x̄) = 7.571428571
Standard deviation = 1.296974501
We can calculate the critical value and test value based on this information.
1. Critical Value:
The critical value is obtained from the t-distribution tables or using statistical software. For this hypothesis test, we assume a significance level (α) of 0.05 or 5%.
Since the alternative hypothesis is one-tailed (x̄ > 8), we look for the critical value in the upper tail of the t-distribution. The degrees of freedom for this test would be n - 1, where n is the sample size.
Using the t-distribution table or software, with a significance level of 0.05 and degrees of freedom n-1, find the critical value corresponding to the upper tail probability. Let's assume we have a sample size of 22 (as shown in your data). Therefore, the degrees of freedom would be 21.
2. Test Value:
The test value is obtained by calculating the t-statistic using the formula:
t = (x̄ - μ) / (s / √n)
Where:
x̄ is the sample mean
μ is the population mean under the null hypothesis (H0)
s is the sample standard deviation
n is the sample size
In our case:
x̄ = 7.571428571
μ = 8 (the value mentioned in H0)
s = 1.296974501
n = 22 (the sample size mentioned in your data)
Plug these values into the formula to calculate the test value.
Once you have both the critical value and the test value, you can compare them to make a decision regarding the null hypothesis.