Some Help Please

Mean 266 Days
STD=16 Days

Question 1-

What is the probability that a random sample of 20 pregnancies that has a mean gestation period of 260 days or less?

So let me first solve it.

16/√20=3.578

260-266/3.578=-1.676 and it will become = .0465

Question 2

What is the probability that random sample of 50 pregnancies that a has mean gestation of 260 or less.

Same steps as above and the answer will be .0040.


Okay.... For the first question the answer in the book states... If we take a 100 simple randm sample of size n=20 human pregnancies then about 5 of the sameples result in a mean gestation period of 260 or less.

2nd question.. If we take a 1000(yes, 1,000) random samples of size n=50...... And etc(same type of summary explained)


Okay, my question is where is the 100 simple random sample, and 1,000 Random Samples coming from?

Good work - I added some notations to make it more readable.

PSG said:

Mean 266 Days
STD=16 Days

Question 1-

What is the probability that a random sample of 20 pregnancies that has a mean gestation period of 260 days or less?

So let me first solve it.

16/√20=3.578 = standard deviation of sample means

(260-266)/3.578=-1.676 = z, and probability = .0465 ~ 5%

Question 2

What is the probability that random sample of 50 pregnancies that a has mean gestation of 260 or less.

Same steps as above and the answer will be .0040.


Okay.... For the first question the answer in the book states... If we take a 100 simple randm sample of size n=20 human pregnancies then about 5 of the sameples result in a mean gestation period of 260 or less.

2nd question.. If we take a 1000(yes, 1,000) random samples of size n=50...... And etc(same type of summary explained)


Okay, my question is where is the 100 simple random sample, and 1,000 Random Samples coming from?

Click to expand...

From lots and lots of doctor and hospital records! 1000 samples of 50 each is 50,000 pregnancies. Since these have to be statistically random, they have to come from more than one mother.

DrPhil said:

Good work - I added some notations to make it more readable.
From lots and lots of doctor and hospital records! 1000 samples of 50 each is 50,000 pregnancies. Since these have to be statistically random, they have to come from more than one mother.

Click to expand...

Okay, thanks! So, you can pick a random number like 100 or 1000? For example, the first question could've been the 1000 and the second the 100? These numbers are just randomly picked?

PSG said:

Okay, thanks! So, you can pick a random number like 100 or 1000? For example, the first question could've been the 1000 and the second the 100? These numbers are just randomly picked?

Click to expand...

They are supposedly picked by a researcher trying to do surveys. One of the first steps in performing a study is to set up the size of the samples. "1000 samples of 50 each" is not very practical!

Another factor in designing the experiment or survey is how to "guarantee" that the samples are all statistically independent - now do you assure the subjects are selected at random? It is generally not easy.

DrPhil said:

They are supposedly picked by a researcher trying to do surveys. One of the first steps in performing a study is to set up the size of the samples. "1000 samples of 50 each" is not very practical!

Another factor in designing the experiment or survey is how to "guarantee" that the samples are all statistically independent - now do you assure the subjects are selected at random? It is generally not easy.

Click to expand...

Hmm, okay, so for example, if the z and probability is. 0400, I'd use 100. And if its, .0040, I would use 1000? We try to get close to a whole number?

I kinda of have a follow up question.

What Might you conclude if a random sample of 50 pregnancies resulted in a mean gestation period if 260 days or less?

The answer to this is.. This result would be unusual, so the sample likely came from a population whose mean gestation period is less than 266 days.

It has the same mean and STD... And I solved it, it was part of the second question I believe. ... Why would this be unusual? Is it because it was under the .05%?

PSG said:

Hmm, okay, so for example, if the z and probability is. 0400, I'd use 100. And if its, .0040, I would use 1000? We try to get close to a whole number?

I kinda of have a follow up question.

What Might you conclude if a random sample of 50 pregnancies resulted in a mean gestation period if 260 days or less?

The answer to this is.. This result would be unusual, so the sample likely came from a population whose mean gestation period is less than 266 days.

It has the same mean and STD... And I solved it, it was part of the second question I believe. ... Why would this be unusual? Is it because it was under the .05%?

Click to expand...

Another part of designing the survey is to decide ahead of time how large a deviation musty be before you reject the hypothesis that the deviation is random. For instance, you can be "95% confident" that a sample mean will not be less than 1.645 standard deviations below the mean. Using the 95% confidence interval, in your first example you would not "reject the hypothesis" that the mean is 266 days.

In the second example, however, you would reject the null hypothesis in favor of an alternate hypothesis that the sample mean is really less than 266 days. Specifically, you found that the probability of having a sample mean as low as observed just because of random fluctuations is only 0.4%.