Question

A sample of five measurements, randomly selected from a normally distributed population, resulted in the summary statistics xˉ=4.7 and s =1.2. Complete parts a through c below. a. Test the nuil hypothesis that the mean of the population is 6 against the allernative hypothesis, μ<6. Use α=0.05 The test statiste is (Round to two decimal places as needed.)

Answer 1

To test the null hypothesis that the mean of the population is 6 against the alternative hypothesis μ<6, we will use a one-sample t-test. The test statistic obtained is -2.57.

Step-by-step explanation:

To test the null hypothesis that the mean of the population is 6 against the alternative hypothesis μ<6, we will use a one-sample t-test. However, we will use a t-test instead of a z-test because we don't know the population standard deviation.

First, we calculate the t-test statistic using the formula:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (4.7 - 6) / (1.2 / √5)

Now, we can calculate the t-test statistic using the given values:

t = -2.57

Therefore, the test statistic for this hypothesis test is -2.57.