A random sample of 36 coffee bags has $\bar{x}=502$ g and $s=12$ g. A roaster tests $H_0:\mu =500$ against $H_a:\mu >500$. What is the t statistic, to two decimals?

A bottling check uses 25 bottles with $\bar{x}=494$ mL and $s=10$ mL to test $H_0:\mu =500$ against $H_a:\mu <500$. What is the t statistic, to two decimals?

A farm samples 16 seedlings with $\bar{x}=18.6$ cm and $s=2.4$ cm, testing $H_0:\mu =17.4$ against $H_a:\mu >17.4$. What is the t statistic, to two decimals?

A bus route study samples 49 trips with $\bar{x}=42.8$ min and $s=7.0$ min, testing $H_0:\mu =45$ against $H_a:\mu \ne 45$. What is the t statistic, to two decimals?

A lab tests 64 tablets with $\bar{x}=9.85$ g and $s=0.40$ g, testing $H_0:\mu =10.00$ against $H_a:\mu <10.00$. What is the t statistic, to two decimals?

A cafeteria samples 25 soup cups with $\bar{x}=251$ mL and $s=5$ mL, testing $H_0:\mu =250$ against $H_a:\mu >250$. What is the t statistic, to two decimals?

An orchard samples 9 apples with $\bar{x}=155$ g and $s=12$ g, testing $H_0:\mu =160$ against $H_a:\mu <160$. What is the t statistic, to two decimals?

A clinic samples 15 patients with $\bar{x}=74.1$ beats/min and $s=8.3$, and the display is roughly symmetric with no outliers. The nurse tests whether the mean differs from 72. Which setup is correct?

A factory samples 12 bolt lengths with $\bar{x}=30.4$ mm and $s=0.5$ mm to test whether $\mu$ differs from 30 mm; the dot plot is strongly skewed with a high outlier. What condition judgment is best?

A school samples 50 backpacks with $\bar{x}=6.8$ kg and $s=1.9$ kg to test $H_0:\mu =7$ against $H_a:\mu <7$. The distribution is mildly skewed. Why is a t test still reasonable?

A water lab samples 20 sites with $\bar{x}=9.2$ mg/L and $s=1.5$ mg/L to test whether the mean nitrate level is below 10 mg/L. The sample is random with no outliers. Which hypotheses fit?

A paint shop samples 18 cans with $\bar{x}=73.2$ mL and $s=4.5$ mL, testing $H_0:\mu =75$ against $H_a:\mu <75$. The test gives $t=-1.70$. What df and p-value area are used?

A machine samples 30 parts with $\bar{x}=101.3$ g and $s=5.2$ g, testing $H_0:\mu =100$ against $H_a:\mu \ne 100$. The test gives $t=1.37$. What df and p-value area are used?

A nursery samples 12 planters with $\bar{x}=4.6$ L and $s=0.7$ L, testing $H_0:\mu =4.2$ against $H_a:\mu >4.2$. The test gives $t=1.98$. What df and p-value area are used?

A delivery study samples 41 trips with $\bar{x}=18.7$ min and $s=3.8$ min, testing $H_0:\mu =20$ against $H_a:\mu \ne 20$. The test gives $t=-2.19$. What df and p-value area are used?

Milk cartons should average 250 mL. A random sample of 22 cartons has $\bar{x}=247.8$ mL and $s=4.9$ mL; $t=-2.11$, df = 21, two-sided p-value = 0.047. At $\alpha =0.05$, what is the conclusion?

Metal rods should average 50 cm. A random sample of 16 rods has $\bar{x}=50.6$ cm and $s=1.2$ cm; $t=2.00$, df = 15, p-value = 0.032 for $H_a:\mu >50$. At $\alpha =0.01$, what is the conclusion?

Paper strength is supposed to average 80 N. A random sample of 28 sheets has $\bar{x}=82.4$ N and $s=5.6$ N; $t=2.27$, df = 27, two-sided p-value = 0.031. At $\alpha =0.05$, what is the conclusion?

A coach tests whether mean recovery time is under 10 min. A random sample of 14 athletes has $\bar{x}=9.1$ min and $s=1.8$ min; $t=-1.87$, df = 13, p-value = 0.042. At $\alpha =0.10$, what is the conclusion?

A river study tests whether mean pH differs from 7.0. A random sample of 25 sites has $\bar{x}=7.1$ and $s=0.4$; $t=1.25$, df = 24, two-sided p-value = 0.224. At $\alpha =0.05$, what is the conclusion?