# conducting a two-sided test at the α= 0.05 level of significance

#### Reels

##### New Member
Hey guys i assume this is probably a really basic question, but its giving me trouble. I have only recently taken up stat study and have a limited maths background.
So anyway as the title states i have to conduct a two-sided test given the following info:

Population Standard Deviation = 9.2
Sample Mean = 85
Population Mean = 76.4
Level of significance = 0.05
Sample Size = 25
Degrees of Freedom = 24

So i tried to calculate the z-stat, using (85-76.4)/(9.2/sqrt(25)) = 4.7
I'm not sure what i have done wrong but im fairly sure the z-stat shouldn't be that big.

#### vinux

##### Dark Knight
You have done it correctly.

since here, the difference between pop. mean and sample mean is high.. so you can expect high value of z value.

#### Reels

##### New Member
Thanks vinux!
Is it right to then that the p-value will be <0.001 and therefore I can regect the null hypothesis?
Also I am asked to calculate the 95% confidence interval for the point estimate.
Would i do this by x +- (4.7x9.2)/sqrt(25) = +- 8.65?

#### vinux

##### Dark Knight
Yes.. The p value will be

P(Z>4.7)*2 ( since it is 2 sided) where Z follows standard normal distribution . you will get the pvalue ..very close to zero( so you can wrte <0.001 ) and you can reject the null hypothesis.

I am not clear about the question about CI for the point estimate.

#### Reels

##### New Member
Thanks again Vinux,

Sorry about my CI question, with my limited knowledge of stats I'm not sure how to re-word the question. Here is the question:
The distribution of diastolic blood pressures for the population of women with diabetes
between the ages of 30 and 34 has an unknown mean μ and standard deviation of σ =
9.2 mm Hg. It may be useful to physicians to know whether the mean of this population
is equal to the mean diastolic blood pressure of the general population of females in this
age group, 76.4 mm Hg.
a) What are the null and alternative hypotheses of the appropriate test? Completed

b) A sample of 25 women aged 30 to 34 years with diabetes is selected; their mean
diastolic blood pressure is 85 mm Hg. Using the information given conduct a two-sided
test at the α= 0.05 level of significance. Completed above

c) What is the 95% confidence interval for this point estimate and p-value of the test? I have the p-value but am unsure how to calculate the CI

#### vinux

##### Dark Knight
95% confidence interval for the population mean is

sample mean +/- 1.96 * standard deviaton/sqrt(sample size)

ie 85+/- 1.96 *9.2/5

Here 1.96 is the value correspond to 95% siginificance level.
ie P(-1.96<Z<1.96) =0.95