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sladkih [1.3K]
3 years ago
15

In Pennsylvania the average IQ score is 101.5. The variable is normally distributed, and the population standard deviation is 15

. A school superintendent claims that the students in her school district have an IQ higher than the average of 101.5. She selects a random sample of 30 students and finds the mean of the test scores is 106.4. Test the claim at ???? = 0.05.
Mathematics
1 answer:
blsea [12.9K]3 years ago
5 0

Answer:

We conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101.5

Sample mean, \bar{x} = 106.4

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 15

First, we design the null and the alternate hypothesis

H_{0}: \mu = 101.5\\H_A: \mu > 101.5

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{106.4 - 101.5}{\frac{15}{\sqrt{30}} } = 1.789

Now, z_{critical} \text{ at 0.05 level of significance } = 1.96

Since,  

z_{stat} > z_{critical}

We reject the null hypothesis and accept the alternate hypothesis.

Thus, we conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

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