Question 257773: Question:
3.A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is cheating its customers. The agency select 20 of these bottles, measures their contents, and obtains a sample mean of 11.7 ounces with a standard deviation of 0.70 ounce. Assume the distribution is normally distributed. Test the agency’s claim that the brewery is cheating its customers
a. Use the critical value t0 method from the normal distribution to test for the population mean -symbol is a mean. Test the agency’s claim at the level of significance -symbol is significance of alpha = 0.05.
1. H0 :
Ha :
2. = significance of alpha symbol
3. Test statistics:
4. P-value or critical z0 or t0.
5. Rejection Region:
6. Decision:
7. Interpretation:
b. Use the critical value t0 method from the normal distribution to test for the population mean -symbol is a mean. Test the agency’s claim at the level of significance -symbol is signficance of alpha = 0.01
1. H0 :
Ha :
2. -symbol is a significance of alpha = 0
3. Test statistics:
4. P-value or critical z0 or t0.
5. Rejection Region:
6. Decision:
7. Interpretation:
I have tried to understand this chapter but no luck.
Answer by onlinetutor365.com(14)   (Show Source):
You can put this solution on YOUR website! A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is cheating its customers. The agency select 20 of these bottles, measures their contents, and obtains a sample mean of 11.7 ounces with a standard deviation of 0.70 ounce. Assume the distribution is normally distributed. Test the agency’s claim that the brewery is cheating its customers
a. Use the critical value t0 method from the normal distribution to test for the population mean. Test the agency’s claim at the level of significance = 0.05.
1. H0 : µ=12
Ha : µ < 12 (because the problem claims there is cheating which is less than 12)
2. =0.05
3. Test statistics:
t= (11.7-12)/[0.7/square root(20) = -1.92
4. P-value or critical z0 or t0.
The critical value of to=-1.729
5. Rejection Region:
12
-1.729 t-score
6. Decision:
Since test statistic of t=-1.92 <-1.729, we reject the null hypothesis.
7. Interpretation:
We conclude that there is significant evidence of the manufacturer's claim and provides strong evidence that the brewery is cheating
b. Use the critical value t0 method from the normal distribution to test for the population mean. Test the agency’s claim at the level of significance = 0.01
(References: example 1 though 5 pages 397 - 401, end of section exercises 23 – 28 pages 404 - 405) (5 points)
1. H0 : µ=12
Ha : µ < 12 (because the problem claims there is cheating which is less than 12)
2. =0.05
3. Test statistics:
t= (11.7-12)/[0.7/square root(20) = -1.92
4. P-value or critical z0 or t0.
The critical value of to=-1.729
5. Rejection Region:
12
-2.539 t-score
6. Decision:
Since test statistic of t=-1.92 >-2.539, we fail to reject the null hypothesis.
7. Interpretation:
We conclude that there is no significant evidence of the manufacturer's claim and provides strong evidence that the brewery is cheating
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