Means

Increase the sample size to at least 30 to rely on the Central Limit Theorem.

Proceed with the t-test, as the t-test is robust to non-normality.

Transform the data to reduce skewness and remove outliers, then proceed with the t-test.

Use a z-test instead of a t-test since z-tests are more accurate with non-normal data.

$\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$

$\bar{x} \pm t^* \frac{\sigma}{\sqrt{n}}$

$\bar{x} \pm z^* \frac{s}{\sqrt{n}}$

$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$

The sample size is at least 30.

The population size is known.

The sample is a random sample from the population.

The population standard deviation is known.

The sample mean.

The population standard deviation.

The alternative hypothesis (one-sided or two-sided).

The sample size.

Fail to reject the null hypothesis; there is not sufficient evidence that the average weight loss is greater than 5 pounds.

Reject the null hypothesis; there is sufficient evidence that the average weight loss is greater than 5 pounds.

Accept the null hypothesis; the average weight loss is equal to 5 pounds.

Reject the null hypothesis; there is sufficient evidence that the average weight loss is equal to 5 pounds.

One-sample t-test

Two-sample t-test

Paired t-test

Z-test

The population of college students at the university must be normally distributed.

The sample size must be less than 10% of all college students at the university.

The population standard deviation must be known.

The sample mean must be equal to the population mean.

95% of all women have heights between 63 and 65 inches.

We are 95% confident that the true average height of women falls between 63 and 65 inches.

There is a 95% probability that the true average height of women is between 63 and 65 inches.

If we take many samples, 95% of the calculated confidence intervals will contain the true average height of women.

It makes the t-distribution more skewed.

It makes the t-distribution flatter and with thicker tails.

It makes the t-distribution identical to the standard normal (z) distribution.

It makes the t-distribution more closely resemble the standard normal (z) distribution.

150 ± 3.16 grams

150 ± 6.32 grams

150 ± 5.05 grams

150 ± 10.10 grams