The distribution of cholesterol levels of the residents of a state closely follows the normal curve. Investigators want to test whether the mean cholesterol level of the residents is 200 mg/dL or lower. A simple random sample of 12 residents has a mean cholesterol level of 185 mg/dL, with an SD of 20 mg/dL (computed as the ordinary SD of a list of 12 numbers, with 12 in the denominator).

Let m be the mean cholesterol level of the residents of the state, measured in mg/dL. Perform a t test of the hypotheses

Null: m = 200 Alternative: m

Question

The distribution of cholesterol levels of the residents of a state closely follows the normal curve. Investigators want to test whether the mean cholesterol level of the residents is 200 mg/dL or lower. A simple random sample of 12 residents has a mean cholesterol level of 185 mg/dL, with an SD of 20 mg/dL (computed as the ordinary SD of a list of 12 numbers, with 12 in the denominator).
 
Let m be the mean cholesterol level of the residents of the state, measured in mg/dL. Perform a t test of the hypotheses
 
Null: m = 200                     Alternative: m < 200

anonymous · Answer

The value of the t statistic is closest to ?

anonymous · Answer

The P-value of the test is closest to?

amistre64 · Answer

t test uses the t distribution charts .... its a one tailed test it looks like; df = 11

amistre64 · Answer

the test statistic i believe is still calulcated the same ... just uses a different table to assess?

amistre64 · Answer

t stat = sqrt(12)*(185 - 200)/20 = -2.6 it looks like

anonymous · Answer

Yea ttest i found it is very simple. You are correct!

amistre64 · Answer

the t tables in the back give approxiamtions;  id have to look up the syntax for my ti83 to be ore exacting :)

anonymous · Answer

the t statistic is not -2.6

amistre64 · Answer

200 - 185 then?

anonymous · Answer

i do not know maybe i will try to think later because now i burnt my brain ;p

anonymous · Answer

-2,5980762113533159402911695122588

anonymous · Answer

i dont understand why -2.6 is wrong

amistre64 · Answer

when n<30  t stat uses  (sample mean - population mean), divided by sample sd/sqrt(sample size)

amistre64 · Answer

t = (185 - 200)/(20/sqrt(12))

since its to the left that would cumulate -9999, -2.5981, 11

amistre64 · Answer

is the sd wrong by chance?  wouldnt sample sd be calculated dividing by 11 instead?

amistre64 · Answer

sqrt( sum of squares) / 12 = 20

sqrt( sum of squares) = 12(20)

divide by 11 for sample sd?  just wondering

amistre64 · Answer

$$\sqrt{\frac{\sum (x-\bar x)^2}{12}}=20$$
$$\frac{\sum (x-\bar x)^2}{12}=20^2$$
$$\sum (x-\bar x)^2=12(20^2)$$
divide by 11 and sqrt for sample sd?

amistre64 · Answer

so maybe .. t = -2.487 ... ?

anonymous · Answer

sorry amistre64.  I have to review a paper until tommorow.... i do not know at this moment.. Maybe you are right.,  I will try it later or tommorrow.. if you think something else tell me...

amistre64 · Answer

i think thats all i can muster at the moment for this as well;  i find it odd that they would describe how the SD was calculated if it was not pertinent.

anonymous · Answer

If the population size is not given, you can assume that the correction factor for standard errors is close enough to 1 that it does not need to be computed.

Please use the 5% cutoff for P-values unless otherwise instructed in the problem.