Exam 7: Sampling Distributions

Defective Items Narrative Suppose a sample of 120 items is drawn from a population of manufactured products and the number of defective items is recorded. Prior experience has shown that the proportion of defectives is 0.05. -Refer to Defective Items Narrative. Calculate the upper and lower control limits for a p chart.

If a process is in control, we expect all the data values to fall within one standard deviation of the mean.

Food Expenditures Narrative The amount of money spent on food per week by a Canadian family is known to have a mean of $92 and a standard deviation of $9. Suppose a random sample of 81 families is taken and their sample mean food expenditure is calculated. -Refer to Food Expenditures Narrative. Find the probability that the sample mean, , does not exceed $90.40.

Examination Times Narrative The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed. -Refer to Examination Times Narrative. What is the probability this sample produces an average of less than 50 minutes?

A stratified random sample is useful when the population to be sampled is known to contain two or more mutually exclusive and clearly distinguishable subgroups or strata that differ greatly from one another with respect to some characteristic of interest.

Childcare Amounts Paid Narrative The distribution of the amount spent for childcare in a city has a mean of $675 and a standard deviation of $80. A random sample of 64 families paying for childcare is selected. -Refer to Childcare Amounts Paid Narrative. Find the probability that the sample mean is between $645 and $700.

All sampling plans involve random selection of the sample from the corresponding population.

Recall the rule of thumb used to indicate when the normal distribution is a good approximation of the sampling distribution for the sample proportion, . For the combination n = 25, p = 0.05; the rule is satisfied.

Quota sampling, in which the makeup of the sample must reflect the makeup of the population on some preselected characteristics, often has a non-random component in the selection process.

As the sample size increases, the standard error of the sample proportion decreases.

Rh-Positive Blood Type Narrative The proportion of individuals with an Rh-positive blood type is 88%. You have a random sample of n = 500 individuals. -Refer to Rh-Positive Blood Type Narrative. Is the distribution of approximately normal? Justify your answer.