Question

Consider the following hypothesis test: H 0: 20 H a: < 20 A sample of 60 provided a sample mean of 19.5. The population standard deviation is 1.8. a. Compute the value of the test statistic (to 2 decimals). If your answer is negative, use minus "-" sign. b. What is the p-value (to 3 decimals)? c. Using = .05, can it be concluded that the population mean is less than 20? d. Using = .05, what is the critical value for the test statistic (to 3 decimals)? If your answer is negative, use minus "-" sign.

Answer 1

We reject the null hypothesis and accept the alternate hypothesis. Thus, it be concluded that the population mean is less than 20.

Explanation:

We are given the following in the question:

Population mean, μ = 60

Sample mean,
`\bar{x}` = 19.5

Sample size, n = 60

Alpha, α = 0.05

Population standard deviation, σ = 1.8

First, we design the null and the alternate hypothesis

`H_(0): \mu = 20\\H_A: \mu < 20`

We use One-tailed z test to perform this hypothesis.

Formula:

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

Putting all the values, we have

`z_(stat) = \displaystyle(19.5 - 20)/((1.8)/(√(60)) ) = -2.151`

Now,
`z_(critical) \text{ at 0.05 level of significance } = -1.64`

Since,

`z_(stat) < z_(critical)`

We reject the null hypothesis and accept the alternate hypothesis. Thus, it be concluded that the population mean is less than 20.