Statistics - Hypothesis Testing Projects

The mean length for motor-vehicle-theft offenders in Australia is 16.7 months. One hundred randomly selected

The mean length for motor-vehicle-theft offenders in Australia is 16.7 months. One hundred randomly selected motor-vehicle-theft offenders in Sydney, Australia, had a mean length of imprisonment of 17.8 months. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean length of imprisonment for motor-vehicle-theft offenders in Sydney differs from the national mean in Australia? Assume that the population standard deviation of the lengths of imprisonment for motor-vehicle-theft offenders in Sydney is 6.0 months.
A study assessed fatigue in steel-plant workers due to heat stress. A random sample of 29 casting workers had a mean post-work heart rate of 78.3 beats per minute (bpm). At the 5% significance level, do the data provide sufficient evidence to conclude that the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm? Assume that the population standard deviation of post-work heart rates for casting workers is 11.2 bpm.
According to the Bureau of Labor Statistics , the average consumer spent $1736 on apparel and services in 2012. That same year, 25 consumer units in the Northeast had annual expenditures with a sample mean of $1922.76 and sample standard deviation of $350.90. At the 5% significance level, do the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1736?
The ankle brachial index (ABI) compares the blood pressure of a patient’s arm to the blood pressure of the patient’s leg. A healthy ABI is 0.9 or greater. In a recent study, researchers obtained the ABI of 187 women with peripheral arterial disease. The results were a mean ABI of 0.64 with a standard deviation of 0.15. At the 1% significance level, do the data provide sufficient evidence to conclude that, on average, women with peripheral arterial disease have an unhealthy ABI?

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