Complete the following hypothesis test where x is a normal random variable and i

Question

Complete the following hypothesis test where x is a normal random variable and is known using the z test.

Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took glucose readings once a week and found a sample mean of x = 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that = 12.5. The mean glucose for horses should be µ = 85 mg/100ml. Doe these data indicate that Gentle Ben has an overall average glucose level higher than 85. Use a 0.05 level of significance.

Explanation / Answer

Hypothesis:

H0: µ= 85

H1: µ> 85; right-tailed test

Test statistic:

z = 8*(93.9 - 85)/12.5

z = 1.99

The P-Value is 0.023295.
A small p-value (typically 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

So, data indicate that Gentle Ben has an overall average glucose level higher than 85.

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