Let's set up a null and alternative hypothesis, find a formula, then go from there.
Null hypothesis:
Ho: µ = 20.5 -->meaning: population mean is equal to 20.5
Ha: µ < 20.5 -->meaning: population mean is less than 20.5
Using the z-test formula to find the test statistic:
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)
z = (19.5 - 20.5)/(2.3/√30)
Calculate the z-test statistic and draw your conclusions. Remember if the null is not rejected, there is no difference. If the null is rejected, there is a difference.
I hope this will help.
2. Herpetologists (snake specialists) found that a certain species of reticulated python have an average length of 20.5 feet with a standard deviation of 2.3 feet. The scientists collect a random sample of 30 adult pythons and measure their lengths. In their sample the mean length was 19.5 feet long. One of the herpetologists fears that pollution might be affecting the natural growth of the pythons. Do you think this sample result is unusually small?
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