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# Distribution; Standard Deviation; Mean; Confidence Interval

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1. Give the formula for the appropriate test statistic, if any, for the following hypothesis testing situations {see attachment}

2. A federal agency responsible for enforcing laws concerning weights and measures routinely inspects packages to determine whether the weight of the contents is at least as great as that advertised on the package. A random sample of 25 observations of a product whose container claims that the net weight is 10 oz. yielded the a mean of 10.52 oz. and a variance of 1.43.
a) Do these data provide sufficient evidence to enable the agency to conclude that the true mean net weight exceeds the net weight indicated on the container. Use &#945; = .10. Make sure you give the conditions under which this test is valid.
b) Estimate with 95% confidence the mean weight of the container. Make sure you give the conditions under which this confidence interval is valid.

https://brainmass.com/statistics/students-t-test/distribution-standard-deviation-mean-confidence-interval-29414

#### Solution Preview

Practice Problems

1. Give the formula for the appropriate test statistic, if any, for the following hypothesis testing situations.
a) n = 20, s = 45 population normally distributed
since the only the sample standard deviation "s" is known, and the sample size is not very large, we use the student t-test.
First compute the sample standard error SE = s / SQRT(n), where (SQRT is square root)
Let sample mean = m, then compute:
t = (sample mean - &#956;o) / standard error = (m - &#956;o) / SE = (m - &#956;o) / [s / SQRT(n)]
t = (m - &#956;o) * SQRT(n) / s

b) n = 80, &#963; = 29 population not normal
The t-test is used when the sample observations are normally distribution or near normal, but it is performs quite well even when the population/sample distribution is highly non-normal (this property is called robustness).
Again, we use t test:
t = (m - &#956;o) * SQRT(n) /&#963;
Some statisticians argues that when sample size is large, ...

#### Solution Summary

1. Give the formula for the appropriate test statistic, if any, for the following hypothesis testing situations Give the formula for the appropriate test statistic, if any, for the following hypothesis testing situations.

a) n = 20, s = 45 population normally distributed
b) n = 80, &#963; = 29 population not normal
c) n = 15, &#963; = 25 population not normal
d) n = 15, s = 36 population not normal
e) n = 10, &#963; = 16 population normal
f) n = 60, &#963; = 81 population normal
g) n = 200, s = 25 population not normal

2. A federal agency responsible for enforcing laws concerning weights and measures routinely inspects packages to determine whether the weight of the contents is at least as great as that advertised on the package. A random sample of 25 observations of a product whose container claims that the net weight is 10 oz. yielded the a mean of 10.52 oz. and a variance of 1.43.
a) Do these data provide sufficient evidence to enable the agency to conclude that the true mean net weight exceeds the net weight indicated on the container. Use &#945; = .10. Make sure you give the conditions under which this test is valid.
b) Estimate with 95% confidence the mean weight of the container. Make sure you give the conditions under which this confidence interval is valid.

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