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jeyben [28]
3 years ago
7

Use the t-distribution and the sample results to complete the test of the hypotheses. Use a significance level. Assume the resul

ts 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.
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
3 0

Answer:

Test statistic = 1.3471

P-value = 0.1993

Accept the null hypothesis.

Step-by-step 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 \neq 4

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

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{4.8 - 4}{\frac{2.3}{\sqrt{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.

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