Question

Use the t-distribution and the sample results to complete the test of the hypotheses. Use a significance level. Assume the results come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal.Test H0: μ= 4 vs Ha: μ≠4 using the sample results x= 4.8, s= 2.3, with n= 15.Give the test statistic and the p-value.

Answer 1

Test statistic = 1.3471

P-value = 0.1993

Accept the null hypothesis.

Explanation:

We are given the following in the question:

Population mean, μ = 4

Sample mean,
`\bar{x}` = 4.8

Sample size, n = 15

Alpha, α = 0.05

Sample standard deviation, s = 2.3

First, we design the null and the alternate hypothesis

`H_(0): \mu = 4\\H_A: \mu \\eq 4`

We use two-tailed t test to perform this hypothesis.

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(s)/(√(n)) }`

Putting all the values, we have

`t_(stat) = \displaystyle(4.8 - 4)/((2.3)/(√(15)) ) = 1.3471`

Now, we calculate the p-value.

P-value = 0.1993

Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept it.