Solve -7y=42 What is y?
2 answers:
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Answer:
We conclude that the null hypothesis is rejected which means residents of Legacy Ranch use less water on average.
Step-by-step explanation:
We are given that the American Water Works Association reports that the per capita water use in a single-family home is 67 gallons per day.
Twenty-three owners responded, and the sample mean water use per day was 63 gallons with a standard deviation of 8.1 gallons per day.
<u><em>Let </em></u><u><em> = average water usage by residents of Legacy Ranch.</em></u>
So, Null Hypothesis, :
67 gallons {means that the residents of Legacy Ranch uses more or equal to 67 gallons water on average}
Alternate Hypothesis, :
< 67 gallons {means that the residents of Legacy Ranch use less water on average}
The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about population standard deviation;
T.S. = ~
where, = sample mean water use per day = 63 gallons
s = sample standard deviation = 8.1 gallons
n = sample of responded = 23
So, <u><em>test statistics</em></u> = ~
= -2.368
The value of the test statistics is -2.368.
<em>Now at 0.025 significance level, the </em><u><em>t table gives critical value of -2.074 at 22 degree of freedom for left-tailed test</em></u><em>. Since our test statistics is less than the critical values of t as -2.368 < -2.074, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to </em><u><em>which we reject our null hypothesis</em></u><em>.</em>
Therefore, we conclude that the residents of Legacy Ranch use less water on average.
The image shows that all integers are rational numbers, but there are rational numbers that are not integers.
The formal statement would be