Basic in Hypothesis Testing A-Level

Theplayfulgirl brainy SG

... Hurahh. I did it.

Anw, I met a problem with this exercise of Hypo:

For a random sample of 10 observations of normal variable X, the mean is x' where x'=4.344

sigma (x-x')^2 =0.8022

Using a 5% significance level, carry out a 2 tailed test whether the mean of X is 4.58

Ho: mu=mu o= 4.58

H1 :mu doesn't equal mu o

I did the same way with my book except one step.

My solution : Because of 5% significance level, reject Ho if z< -1.9599 or z>1,9599

Book solution: 5% critical value, t 0,025 ; 9 =2.262

..................

If |t|> t 0.025; 9 reject Ho

My question is

_Whether my solution is wrong and why?

_ What is t 0.025 ; 9.?

What is the meaning of 9?

How to find that value by TI 83?

Thank you

wee_ws SG

Hi,

You used the Z-test which is inappropriate in this case. Since the data comes from a Normal population, n (sample size) is small and population variance is unknown, we will use the T-test instead.

t_{0.025} refers to the t-value that would give an area of 0.025. We consider 0.025 since we are looking at a 2-tailed test at 5% (0.05) level of significance.

9 refers to the degrees of freedom and this is calculated by the formula:

sample size - 1.

The required GC steps are

1. Press 2ND, VARS.

2. Select invT(

3. Enter 0.025, 9.

4. Obtain -2.262... as output.

Thanks.

Cheers,
Wen Shih

Theplayfulgirl brainy SG

For a random sample of 10 observations of normal variable X

So the word normal variable X decide if I'm able to use N test or not..

OMG. Those stuffs are so confusing.

wee_ws SG

Hi,

To use the T-test, we need to have the following conditions met:

1. Population is Normal or assumed to be Normal.

2. Sample size is small.

3. Population variance or standard deviation is unknown.

Thanks.

Cheers,
Wen Shih

Theplayfulgirl brainy SG

Thank you. I got it now

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