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# Statistical Methods Assignment - Research Paper Example

Summary
In a t distribution, as the degree of freedom reaches infinity, the size of the 1% and 5% values of the t are the same as that for z. That is, it reaches 1.96 for 95% critical values and 1.64 for 90% critical values.
The two intervals do not seem to have a significant difference between them…

## Extract of sample"Statistical Methods Assignment"

Download file to see previous pages Since this is a weight reduction study, we did a one-directional t test. Results showed that the diet resulted in a significant decrease in weight, both for a 90% and 95% confidence level.
In both cases, it is reasonable to say that two-thirds of the general population agrees with the principle of University top-up fees. The hypothesized p is included in both intervals. We, therefore, do not reject the null hypothesis.
...
: 0.05 p = 2*0.0096 = 1 - 0.9808 = 0.0192

The test shows that there is a significant statistical difference between the sample mean and the hypothesized mean, on a 95% confidence level. We, therefore, reject the null hypothesis.

Question 6

sample size 121 degree of freedom 120
sample mean 47.50 critical t 1.658
sample standard deviation 7.50

90% confidence interval (46.37, 48.63)

Assuming that the population standard deviation is equal to the sample standard deviation, the confidence interval becomes:

(46.38, 48.62)

The two intervals do not seem to have a significant difference between them. This is a result of having a large sample size. As the sample size increases, the difference between the two intervals is also expected to significantly increase, resulting to large errors.

Question 7

t ratio
3.364

alpha ()
critical t

0.05
2.306
reject H0
0.10
1.860
reject H0

In this test, we assume that the sample standard deviation approximates that of the population without any significant statistical difference. Since this is a weight reduction study, we did a one-directional t test. Results showed that the diet resulted in a significant decrease in weight, both for a 90% and 95% confidence level.

Question 8

T
680
N
1050
T/n
0.648
p
0.667
standard deviation
0.228

Test Statistic 1.29
(1.29) 0.9015
p value 0.1970

95% confidence interval (0.619, 0.677)
90% confidence interval (0.623, 0.672)

In both cases, it is reasonable to say that two-thirds of the general population agrees with the principle of University top-up fees. The hypothesized p is included in both intervals. We, therefore, do not reject the null hypothesis.

Question 9

To estimate a population proportion p with a 95% confidence ...Download file to see next pagesRead More
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