Your friend owns a retail store where she plans to pitch arriving customers with a new angle -- a new sales pitch. Impressed by your recently acquired data analysis skills, your friend asks you to determine if this will boost the average sales level, , which is currently $50 per customer. She does not think the new pitch would reduce sales, but who knows, it might if it's a bad pitch! (So without a strong prior, this is a two-tail test!). You can assume from past data that the population standard deviation of transactions is $10 (Again, that is population, not sample!). You monitor N = 200 customers that get the new sales pitch and you record the amount purchased. Assume that = 0.05 (95% confidence). Your friend will keep doing the sales pitch if your sample evidence indicates that it's working. In your sample, you find mean sales to be $52.

What is the null hypothesis?

Group of answer choices

1. New sales are the same as the old sales: mu=50

2. Sales increased from the old sales mu>50

3. Sales have gone down with the new pitch mu<50

The distributions have changed

Using a normal distribution, what is the absolute value of the standardized critical value(s) you should use for this decision? (For example, if you thought it was a one left-tailed test with alpha=10% and the critical value was -1.28 you would put in 1.28, and round to two decimal places).

What is the standardized Z-statistic (based on a normal distribution) for your Hypothesis test based on your sample? (Round to two decimal places so 1.232 would be 1.23).

How does your standardized Z-statistic compare to the critical value?

Assuming a one tailed test (regardless of what you did above) and a normal distribution, what is the p-value associated with your Z-statistic? (Round to four decimal places e.g. 0.0483)

Assuming you found that the absolute value of the test statistic from your sample is larger than the critical value (on either side), what is your decision?

Group of answer choices

Reject the null

Accept the null

Fail to reject the null

Fail to accept the alternative