1) Find the critical value(s) that would be used in a hypothesis test of the fol
ID: 3259112 • Letter: 1
Question
1) Find the critical value(s) that would be used in a hypothesis test of the following claim.
Claim: "The mean amount of beverage in a medium drink sold at this college's cafeteria is less than 20 ounces."
A random sample of 101 medium drinks from this cafeteria is collected, and it produces a test statistic of t = -2.89. A significance level of = 0.01 is to be used.
b) Use the critical value(s) that you found in the previous question to test the following claim, and state the conclusion of the hypothesis test.
2) Find the critical value(s) that would be used in a hypothesis test of the following claim.
Claim: "The percentage of Michigan residents who oppose a proposed increase in sales tax to pay for road repairs is not 50%."
A random sample of 725 Michigan residents was collected, and it produced a test statistic of z = -3.58. A significance level of = 0.02 is to be used.
b) Use the critical value(s) that you found in the previous question to test the following claim, and state the conclusion of the hypothesis test
3) Find the P-value that would be used in a hypothesis test of the following claim.
Claim: "The mean concentration of radon gas in American homes is 2.7 pCi/L."
A random sample of the concentration of radon gas in 91 American homes is collected, and it produced a test statistic of t = 2.78. A significance level of = 0.01 is to be used.
b) Use the P-value that you found in the previous question to test the following claim, and state the conclusion
4) Find the P-value that would be used in a hypothesis test of the following claim.
Claim: “This bottling facility under fills more than 5% of bottles.”
A random sample of 600 bottles filled at this facility is selected, and a test statistic of z = 1.98 is calculated. A significance level of a = 0.025 is to be used
b) Use the P-value that you found in the previous question to test the following claim, and state the conclusion.
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Explanation / Answer
Solution:-
1)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 20
Alternative hypothesis: < 20 (The mean amount of beverage in a medium drink sold at this college's cafeteria is less than 20 ounces.)
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
DF = n - 1 = 101 - 1
D.F = 100
t = (x - ) / SE
t = - 2.89
tcritical = - 2.364
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Interpret results. Since the t test value (- 2.89) is less than the tcritical (- 2.364), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that mean amount of beverage in a medium drink sold at this college's cafeteria is less than 20 ounces.
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