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Water! A blogger claims that U.S. adults drink an average of five 8-ounce glasses (that鈥檚 40 ounces) of water per day. Researchers wonder if this claim is true, so they ask a random sample of 24 U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers.

a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

b. Check conditions for performing the test in part (a).

c. The 90% confidence interval for the mean daily water intake is 30.35 to 36.92 ounces. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 10% significance level?

d. Do we have convincing evidence that the amount of water U.S. children drink per day differs from 40 ounces? Justify your answer.

Short Answer

Expert verified

Part (a)H0:=40H1:40

Part (b) All conditions are satisfied.

Part (c) There is convincing proof that the mean daily water intake is different from 40ounces.

Part (d) No.

Step by step solution

01

Part (a) Step 1: Given information

Claim is that the mean is 40 ounces.

02

Part (a) Step 2: Explanation

The null hypothesis asserts that the population value is the same as the claim value:

H0:=40

Either the null hypothesis or the alternative hypothesis is the assertion. The null hypothesis asserts that the population means is the same as the claim value. If the claim is the null hypothesis, the alternative hypothesis statement is the polar opposite of the claim.

H1:40

is the mean daily water intake of U.S. adults.

03

Part (b) Step 1: Explanation

The three conditions are Random, independent, and Normal/ Large sample.

Random: Because the sample is a random sample, I'm satisfied.

Independent: Because the sample of 24 individuals in the United States represents less than 10% of the total adult population in the United States, I am happy.

Normal/Large sample: Satisfied since the data graph reveals no outliers or skewed distribution. Because all of the prerequisites are met, a hypothesis test for the population mean is appropriate.

04

Part (c) Step 1: Given information

90% confidence interval:

(30.35,36.92)

05

Part (c) Step 2: Explanation

A hypothesis test with a significance level of 100%-90%=10% is associated with a 90% confidence interval.

It is noted that the confidence interval does not include 40 implying that the mean daily water consumption is unlikely to be 40 ounces, and so there is convincing proof that the mean daily water intake is not 40 ounces.

06

Part (d) Step 1: Explanation

Because the data is based on adults in the United States, it is impossible to conclude that children in the United States have a different daily water intake than adults.

It signifies that we don't have enough data to believe that the average daily water intake of American youngsters is less than 40 ounces.

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