Question

You are thinking of conducting a one-sample $t$test about a population mean $\mu$using a $0.05$significance level. Which of the following statements is correct?

a. You should not carry out the test if the sample does not have a Normal distribution.

b. You can safely carry out the test if there are no outliers, regardless of the sample size.

c. You can carry out the test if a graph of the data shows no strong skewness, regardless of the sample size.

d. You can carry out the test only if the population standard deviation is known.

e. You can safely carry out the test if your sample size is at least 30 .

Short answer

the correct option is (e) as the sample is taken into account to be large therefore then the Normal/Large sample condition is satisfied.

Step-by-step solution

Step 1:Given information

The conditions for conduction a one- sample test are: Random, $10\%$and Normal/ Large sample.

Step 2:Explaination

a. False, as a result of the Normal/ Large sample can still be satisfied if the sample is large (even if the sample doesn't have a Normal distribution).

b. False, as a result of outliers powerfully have an affect on the sample mean and sample standard deviation, which will then also affect the results of the test (as it uses the sample mean and sample standard deviation).

c. False, as a result of the graph ought to show about to normal distribution and a non- skewed distribution is not essentially approximately a normal distribution.

d. False, as a result of if the population standard deviation is known, and then uses the one-sample $z$test instead of the one-sample $t$test.

e. True,as a result of once the sample size is at least $30$then the sample is taken into account to be large therefore then the Normal/Large sample condition is satisfied.

Hence, the correct option is (e)