Math / Data & Statistics

QuestionA fashion company releases a new line of prom dresses that are all under $\$ 100$ . They claim this is a bargain because the average cost of a prom dress is over $\$ 300$ . A customer decide to test this, and takes a random sample of 25 dresses. She finds the mean is $\$ 250$ with a standard deviation of $\$ 10$ . Assume the population is normally distributed and use $\alpha=0.0$ to test the claim.
Which distribution should be used to test the claim? Z-test for the Mean T-test for the Mean p-distribution c-distribution

Studdy Solution

STEP 1

1. The sample size is $n = 25$ .
2. The sample mean is $\bar{x} = 250$ .
3. The sample standard deviation is $s = 10$ .
4. The population is normally distributed.
5. The significance level is $\alpha = 0.0$ .

STEP 2

1. Determine the appropriate test for the mean.
2. Justify the choice of test based on the given data and assumptions.

STEP 3

Since the population standard deviation is not provided and the sample size is small ( $n < 30$ ), we typically use the t-test for the mean when the population standard deviation is unknown.

STEP 4

The t-test is appropriate here because: - The sample size is small ( $n = 25$ ). - The population standard deviation is unknown. - The population is normally distributed.
The appropriate distribution to use for testing the claim is:
$\text{T-test for the Mean}$

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