Question

Conf Interval (CI) Significance one-tail or two- tail? Sample Mean X Pop mean μ (or est) Nbr Samples (Nbr) Pop or Sample Stddev Std Err of Sample Mean Sig Lower bound z/t prob Sig Upper bound z/t prob (1- sig) Sig Lower Sig Upper z/t Value z/t Value Calc z/t p-value Reject or Accept? given or 1 1 for <>, 2 given or given in given given or Stddev/ use if X < use if X > inv norm inv norm per norm/T Calc z/t & -CI for = calc test calc sqrt(Nbr) μ or two- μ or two- or T func or T func formula func 1- compare tail tail 42. The American Water Works Association reports that the per capita water use Page 303 in a single-family home is 69 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Thirty-six owners responded, and the sample mean water use per day was 64 gallons with a standard deviation of 8.8 gallons per day. At the .10 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?

          Conf
Interval
(CI)
Significance
one-tail
or two-
tail?
Sample
Mean X
Pop mean
μ (or est)
Nbr
Samples
(Nbr)
Pop or
Sample
Stddev
Std Err of
Sample
Mean
Sig Lower
bound z/t
prob
Sig Upper
bound z/t
prob (1-
sig)
Sig Lower Sig Upper
z/t Value z/t Value Calc z/t p-value Reject or
Accept?
given or 1 1 for <>, 2 given or given in given given or Stddev/ use if X < use if X > inv norm inv norm per norm/T Calc z/t &
-CI for = calc test calc sqrt(Nbr) μ or two- μ or two- or T func or T func formula func 1- compare
tail tail
42. The American Water Works Association reports that the per capita water use Page 303
in a single-family home is 69 gallons per day. Legacy Ranch is a relatively
new housing development. The builders installed more efficient water fixtures, such
as low-flush toilets, and subsequently conducted a survey of the residences. Thirty-six
owners responded, and the sample mean water use per day was 64 gallons with a
standard deviation of 8.8 gallons per day. At the .10 level of significance, is that
enough evidence to conclude that residents of Legacy Ranch use less water on
average?

Show more…

conf interval ci significance one tail or two tail sample mean x pop mean or est nbr samples nbr pop or sample stddev std err of sample mean sig lower bound zt prob sig upper bound zt prob 1 12538

Added by Travis F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Paul A.

07/28/2022

Step 1

Sample size (Nbr): $n = 36$ Sample mean: $\bar{x} = 64$ Population mean: $\mu = 69$ Sample standard deviation: $s = 8.8$ Significance level: $\alpha = 0.10$ Show more…

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Conf Interval (CI) Significance one-tail or two- tail? Sample Mean X Pop mean μ (or est) Nbr Samples (Nbr) Pop or Sample Stddev Std Err of Sample Mean Sig Lower bound z/t prob Sig Upper bound z/t prob (1- sig) Sig Lower Sig Upper z/t Value z/t Value Calc z/t p-value Reject or Accept? given or 1 1 for <>, 2 given or given in given given or Stddev/ use if X < use if X > inv norm inv norm per norm/T Calc z/t & -CI for = calc test calc sqrt(Nbr) μ or two- μ or two- or T func or T func formula func 1- compare tail tail 42. The American Water Works Association reports that the per capita water use Page 303 in a single-family home is 69 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Thirty-six owners responded, and the sample mean water use per day was 64 gallons with a standard deviation of 8.8 gallons per day. At the .10 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?

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Transcript

00:01 Once again, welcome to a new problem this time.

00:05 We're dealing with inferential statistics.

00:10 We're dealing with inferential statistics.

00:14 And when it comes to inferential statistics, we have hypothesis testing.

00:23 We have hypothesis testing.

00:25 And under hypothesis testing, we have hypothesis testing for means, where the test statistic, the test statistic is the same as t equals to, the test statistic is either the same as t equals to x bar minus mu, s of a radical n, that's the test statistic.

00:59 And so we have a new problem, and in this problem that we're looking at, we have a new problem.

01:06 The per capita water use for single family homes at 75 gallons per day.

01:15 And this is based off of information provided by the american water works.

01:22 So based on the efficient use of the systems installed, we sample 26 owners and these are the respondents.

01:35 And the sample mean for our water use is 72 gallons per day and the standard deviation happens to be 7 .2 gallons per day.

01:45 At alpha equals to 0 .025, we want to determine if the residents use less water.

01:55 So again, we have the now hypotheses and we are hypothesizing that the amount of water that they use on average is 75 gallons per day.

02:12 And the alternative hypothesis is that they're using less water, so less than 75 gallons per day.

02:23 And the next step is that we're going to compute a test statistic.

02:31 We're going to compute a test statistic...

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