Question

* For large samples one sample t-tests (n >120) use critical t scores of ±1.96 (for 95% confidence level two tailed test) or ±1.65 (for 95% confidence level one tailed test).

* For small samples (n<120) use critical t score obtained from t-distribution table. You will need to calculate degrees of freedom, which is simply the sample size minus 1 (df = n-1) and use an alpha value of .05.

* For comparing means between two samples (regardless of sample sizes), use an independent samples t-test, with a critical t of ±1.96.

In a sample of 100 Oklahoma public schools, it was found that Oklahoma spends 8,097 dollars per pupil per year, with a standard deviation of 220 dollars. The population average of three surrounding states (Arkansas, Kansas, and Missouri) is 10,039 dollars. (these numbers are accurate – taken from most recent available data for 2016 https://ballotpedia.org/Public_education_in_Oklahoma.). Is per pupil spending for all Oklahoma schools less than the surrounding state population average? If you had to voice your concerns to your elected representative about per pupil spending in Oklahoma public schools, what would you tell them?

Answer 1

The hypothesis being tested is:

H0: µ = 10039

Ha: µ < 10039

The test statistic, t = (x - µ)/s/√n

t = (8097 - 10039)/220/√100

t = -88.273

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that per-pupil spending for all Oklahoma schools is less than the surrounding state population average.