# Distribution; Standard Deviation; Mean; Confidence Interval

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 α = .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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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 - μo) / standard error = (m - μo) / SE = (m - μo) / [s / SQRT(n)]

t = (m - μo) * SQRT(n) / s

b) n = 80, σ = 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 - μo) * SQRT(n) /σ

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, σ = 29 population not normal

c) n = 15, σ = 25 population not normal

d) n = 15, s = 36 population not normal

e) n = 10, σ = 16 population normal

f) n = 60, σ = 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 α = .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.

Confidence Interval; Sampling Distribution; Mean and Standard Deviation

1. A parcel service randomly selected 48 packages it received. The sample has a mean weight of 18.6 pounds. Assume that σ = 3.4 pounds. Construct a 90% confidence interval for the true mean weight, μ, of all packages received by the parcel service.

2. A phone company wants to estimate the mean duration of local calls. Assume σ = 3.0. the sample size is 540. Find the margin of error in estimating μ at the 90% level of confidence.

3. The mean and standard deviation for a population are 107 and 14, respectively. Samples of size 49 are selected randomly from the population. Find the mean and standard deviation of the sampling distribution.

4. The weekly earnings of students in one age group are approximately normally distributed with a standard deviation of 36 dollars. A researcher wishes to estimate the mean weekly earnings. Find the sample size needed if she requires a 90% degree of confidence that the sample mean will not differ from the population by more than 3 dollars.

5. A sample of cereal boxes were selected, and their weights in ounces were recorded in the attachment. Determine a 95% confidence interval for the mean weight of cereal in all boxes.

Please see the attachment for correct formatting and complete information.

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