A credit card company estimates that the average credit card balance of Americans is $3,210. A statistics student wants to know whether this is true for citizens of her home town. Which hypothesis test would be most appropriate for addressing this question?
One sample z-test
One sample t-test
Paired-samples t-test
Independent samples t-test
ANOVA
Test of one proportion
Test of two proportions
test of one proportion
One Sample T-Test. This was the right answer on my quiz.
Think about it. Since the Std. Dev is unknown z-test can't be the answer.
The most appropriate hypothesis test for addressing this question would be the One Sample t-test.
The One Sample t-test is used when we want to test whether the mean of a single sample is equal to a specified value (in this case, the average credit card balance of Americans, which is $3,210). This is a suitable test because the statistics student wants to compare the average credit card balance of citizens in her hometown to the national average.
To perform a One Sample t-test, the student would need to collect a sample of credit card balances from her hometown citizens. The sample should be representative and randomly selected to obtain unbiased results. Then, she would calculate the sample mean and standard deviation of the credit card balances.
The null hypothesis (H0) would be that the mean credit card balance in her hometown is equal to $3,210, and the alternative hypothesis (Ha) would be that it is different from $3,210. She would choose the level of significance (e.g., 0.05) to determine the cutoff point for rejecting the null hypothesis.
Using the t-test, the student could calculate the t-statistic and compare it to the critical value from the t-distribution table for the given level of significance and degrees of freedom. If the calculated t-statistic falls outside the critical value range, she would reject the null hypothesis and conclude that the average credit card balance in her hometown is significantly different from $3,210.
It is worth noting that if the student knows the population standard deviation, she could use the One Sample z-test instead, as it assumes a known population standard deviation. However, in most real-world scenarios, the population standard deviation is unknown, and therefore, the One Sample t-test is more commonly used.