1. According to a recent study, the mean cost of a 3 bedroom home costs less in Ohio than in Alabama. You think this information is incorrect. You randomly select 35 homes in each state. In Ohio, the mean cost is $137,400. In Alabama, the mean cost is $135,900. From past studies, the population standard deviation for 3 bedroom homes in Ohio is $3200 and in Alabama is $2800. Is there enough evidence to support your claim at = 0.05?
2. A medical research team conducted a study to test whether a drug lowers the chance of getting diabetes. In the study, 2623 people took the drug and 17.1% got diabetes. Also, 2646 people took a placebo and 18.5% got diabetes. At = 0.05, can you support the claim that the drug lowers the chance of getting diabetes?
3. According to a recent study, the mean cost of a 3 bedroom home costs less in Ohio than in Alabama. You think this information is incorrect. You randomly select 35 homes in each state. In Ohio, the mean cost is $137,400 and the standard deviation is $3200. In Alabama, the mean cost is $135,900 and the standard deviation is $2800. Is there enough evidence to support your claim at = 0.05?
4. A scientist claims that a new diet pill causes weight loss in men. The table shows the weights (in pounds) of six men before taking the diet pill and then one week after taking the diet pill. Is there enough evidence to reject the claim at = 0.05?

Man

1

2

3

4

5

6

Weight (before)

198

236

217

205

211

228

Weight (after)

195

235

215

202

209

223

You use a z-test (two samples) when...

• ₁and₂areknown, the samples are independent, and n₁ 30 and n₂ 30
• you're testing proportions, the samples are independent, and n₁p, n₁q, n₂p, n₂q are all at least 5

You use a t-test (two samples) when...

• ₁and₂are unknown, the samples are independent, and the populations are normally distributed
• both populations are normally distributedandthe samples are dependent

Match the four scenarios above with the four different types of two sample hypothesis tests:

1. Z-test (In StatCrunch: StatZ StatsTwo Sample)
2. T-test (In StatCrunch: StatT StatsTwo Sample)
3. T-test (In StatCrunch: StatT StatsPaired)
4. Proportions test (In StatCrunch: StatProportion StatsTwo Sample)