Question

The amount of water consumed per week by Montana residences is normally distributed with an unknown mean and a standard deviation of 10 gallons. A simple random sample of ten residences has a mean value of gallons. The city of Bozeman claim that the average water consumed in the state of Montana is not 125 gallons. (a) State the null and alternative hypothesis.

Answer 1

The null hypothesis, denoted by H0, represents the status quo or the default assumption. In this case, the null hypothesis is that the average water consumption in Montana residences is 125 gallons per week.

The alternative hypothesis, denoted by Ha, is the hypothesis that the researcher is trying to prove. In this case, the alternative hypothesis is that the average water consumption in Montana residences is not equal to 125 gallons per week.

So, the null and alternative hypotheses for this problem are:

H0: μ = 125 (where μ is the population mean water consumption in Montana residences)

Ha: μ ≠ 125 (where μ is the population mean water consumption in Montana residences)

Note that the alternative hypothesis is a two-tailed hypothesis since we are testing whether the population mean is not equal to 125, which could mean it is either greater or less than 125.