We use a t distribution for inference about a population mean instead of the standard Normal distribution:

a. if we do not know the population mean and must use the sample mean.
b. if the original population does not have a Normal distribution.
c. if we do not have a simple random sample.
d. if we do not know the population standard deviation and must use the sample standard deviation.

Question

13-01-2020
Mathematics

contestada

We use a t distribution for inference about a population mean instead of the standard Normal distribution:

a. if we do not know the population mean and must use the sample mean.
b. if the original population does not have a Normal distribution.
c. if we do not have a simple random sample.
d. if we do not know the population standard deviation and must use the sample standard deviation.

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Answer: d. if we do not know the population standard deviation and must use the sample standard deviation.

Step-by-step explanation:

We use t-distribution is quite similar to distribution of z-score .

The interpretation of t-scores and z-scores are same.

T- distribution is used when the data is not accurately normal and when the population standard deviation is unknown.

In the absence of population standard deviation , we use the standard deviation of the sample.

So , We use a t distribution for inference about a population mean instead of the standard Normal distribution if we do not know the population standard deviation and must use the sample standard deviation.

Hence, the correct option is : d. if we do not know the population standard deviation and must use the sample standard deviation.