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Len [333]
3 years ago
7

Consider the following hypothesis test: H 0: 20 H a: < 20 A sample of 60 provided a sample mean of 19.5. The population stand

ard 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.
Mathematics
1 answer:
viva [34]3 years ago
5 0

Answer:

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

Step-by-step 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}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{19.5 - 20}{\frac{1.8}{\sqrt{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.

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