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Given a sample mean (xbar) of 57 and a population standard deviation sigma (?) of 3.5 from a previous study where n= 35 values, find

Given a sample mean (xbar) of 57 and a population standard deviation sigma (?) of 3.5 from a previous study where n= 35 values, find the z value and p value. The data indicates that the population mean (µ) for the new car Eco Auto is 59 miles per gallon but we think it may be lower based on our data. Test the claim that µ< 59. Hint: Use the P value calculator in the announcements to find the p value. Note: On this one you do not need to attach an excel spreadsheet.

Student Response:

I have: µ=59

Ha: µ<59

You can put this in excel or your calculator

Z=(xbar-µ)/(?/ sqrt n) where xbar=57, µ=59, population standard deviation sigma ? = 3.5 and n=35

=-3.38

Using the z to p value calculator

https://www.socscistatistics.com/pvalues/normaldistribution.aspx

with ?=.05, 1 tailed test and z=-3.38, you get

p=.000362

Since p < .05, you reject the null.


1) A study shows the age of a first time home owner. You believe first time home owners are less than 32 years old. Given a sample mean (xbar) of 27 years and a population standard deviation sigma of 4.4 from a sample of n=120 first time home owners, find the z value and p value. Let a = .05, test the claim that µ < 32 years.


2) Principal Leo claims the students with basket weaving degrees have above average intelligence with an IQ greater than 10 years ago. A random sample of 30 graduates show an IQ average score mean of 100 and sigma of 15. Test the claim that µ>100.

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