A cereal inspector tests boxes from one machine: n=36, x-bar=492 g. The maker claims the mean is 500 g, and the inspector suspects less. At $\alpha =0.05$, what hypotheses fit?

In a school survey, n=200 students and $\hat{p}=0.68$ support a later start. The principal tests whether the population support is above 60% at $\alpha =0.05$. What hypotheses fit?

A clinic samples n=25 visits and finds x-bar=20.1 min. Its old mean wait is 18 min, and managers test for any change at $\alpha =0.01$. What hypotheses fit?

A factory checks n=300 parts and finds $\hat{p}=0.06$ defective. The standard defect rate is 4%, and engineers test whether the population rate is different at $\alpha =0.05$. What hypotheses fit?

A coach samples n=18 runners and finds x-bar=23.2 min for a 5-km route. The old mean was 24 min, and the claim is that training lowers mean time at $\alpha =0.05$. What hypotheses fit?

A farm tests n=16 plots with x-bar=84 kg. The usual mean yield is 82 kg, and the question is whether a fertilizer changes yield in either direction at $\alpha =0.05$. What tail type is needed?

A filling machine has n=40 bottles with x-bar=497 mL. The target is 500 mL, and inspectors test whether the mean fill is less than target at $\alpha =0.05$. What tail type is needed?

A tutoring study has n=120 students with $\hat{p}=0.76$ passing. The old pass rate is 70%, and the test asks whether the population pass rate increased at $\alpha =0.05$. What tail type is needed?

A sensor check uses n=12 readings with x-bar=-0.4 °C error. Technicians test whether the mean error differs from 0 °C at $\alpha =0.05$. What tail type is needed?

A city surveys n=400 residents; 232 favor a recycling fee. It tests at $\alpha =0.05$ whether the population proportion favoring the fee is above 0.50. What procedure fits?

A bakery randomly weighs n=12 loaves; x-bar=502 g and s=8 g, with sigma unknown. It tests at $\alpha =0.05$ whether mean weight differs from 500 g. What procedure fits?

A hospital compares readmission rates for two discharge plans: n=180 with Plan A and n=175 with Plan B. It tests at $\alpha =0.05$ whether the population proportions differ. What procedure fits?

Two labs compare mean calcium content in water: n=14 samples from Lab A and n=16 from Lab B, with x-bars and s values reported. At $\alpha =0.05$, what procedure tests for a mean difference?

A teacher records each of n=22 students' quiz scores before and after a review lesson. At $\alpha =0.05$, the test asks whether mean score changed. What procedure fits?

A drug trial tests $H_0:p=0.40$ against $H_a:p>0.40$ at $\alpha =0.05$ using n=300 patients. A Type I error is made. What happened?

A filter test uses $H_0:\mu =5$ µg/L lead and $H_a:\mu <5$ at $\alpha =0.01$ with n=20 samples. A Type II error is made. What happened?

A smoke detector test sets $H_0$ as clear air and $H_a$ as smoke present. At $\alpha =0.05$, the alarm sounds during a trial when the air is actually clear. What error is this?

A poll tests $H_0:p=0.50$ against $H_a:p>0.50$ at $\alpha =0.05$ with n=600 voters. A Type II error is made. What is the cost?

A factory tests $H_0:p=0.02$ against $H_a:p>0.02$ at $\alpha =0.05$ using n=500 parts. A Type I error is made. What is the cost?

A coin test uses n=100 flips, $\hat{p}=0.60$ heads, and $H_0:p=0.50$. The p-value is 0.03. What does 0.03 mean?

A battery test uses n=20 packs, x-bar=78.2 min, and $H_0:\mu =75$ against $H_a:\mu \ne 75$. The p-value is 0.12. What does 0.12 mean?

A survey tests $H_0:p=0.60$ against $H_a:p>0.60$ with n=150 and $\hat{p}=0.74$. The p-value is 0.008. What does it mean?

A clinic tests $H_0:\mu =12$ min against $H_a:\mu <12$ using n=30 visits and x-bar=11.8 min. The p-value is 0.41. What does 0.41 mean?

A test of a recycling claim gives a p-value of 0.042 using n=250 surveys. At $\alpha =0.05$, what decision follows?

A nutrition label test uses n=18 packages and gives a p-value of 0.081. At $\alpha =0.10$, what decision follows?

A test of mean plant growth gives a p-value of 0.018. What are the decisions at $\alpha =0.01$ and $\alpha =0.05$?

A right-tailed z test of a website change has test statistic $z=1.88$. At $\alpha =0.05$, the critical value is 1.645. What decision follows?

A left-tailed t test on n=20 soil samples has test statistic $t=-2.05$. At $\alpha =0.01$, the critical value is -2.539. What decision follows?

A test asks whether more than 60% of parents support a later start. With n=220, $\hat{p}=0.64$, p-value 0.11, and $\alpha =0.05$, what conclusion is correct?

A clinic tests whether a new process lowers mean wait below 10 min. With n=35, x-bar=8.9 min, p-value 0.004, and $\alpha =0.01$, what conclusion is correct?

A wildlife survey tests whether the proportion of tagged fish differs from 0.30. With n=500, $\hat{p}=0.33$, p-value 0.14, and $\alpha =0.05$, what conclusion is correct?

A battery maker tests whether mean life exceeds 8 hr. With n=28, x-bar=8.4 hr, p-value 0.02, and $\alpha =0.05$, what conclusion is correct?

A calculator output block for a one-sample t test on tire life is shown. What p-value should be compared with $\alpha =0.05$?

A calculator output block compares two discharge-plan proportions. What test statistic is reported?

A calculator output block for a one-sample t test on plant height is shown. What sample size was used?

A mayor claims half of all voters favor a measure. In a random sample of n=250 voters, 130 favor it. For $H_0:p=0.50$, what is z to two decimal places?

A clinic claims 80% of patients keep appointments. In a random sample of n=100 patients, 72 kept appointments. For $H_0:p=0.80$, what is z to two decimal places?

A park survey tests $H_0:p=0.35$. In a random sample of n=400 visitors, 156 bought a pass. What is z to two decimal places?

A tire maker claims mean life is 50,000 km. A random sample of n=16 tires has x-bar=48,200 km and s=2,400 km. What is the one-sample t statistic?

A cafeteria claims its mean serving mass is 350 g. A random sample of n=25 servings has x-bar=362 g and s=30 g. What is the one-sample t statistic?