Exam 9: Statistical Inferences Based on Two Samples

You wish to compute a confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ For two normally distributed populations.Independent random samples of are taken from each population.The relevant sample statistics are n₁ = 10,n₂ = 8,s₁ = 5,and s₂= 7.If we assume the population variances are equal,give a pooled estimate of this common variance.

Recently,a case of food poisoning was traced to a particular restaurant chain.The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur.Despite the response from the restaurant chain,many consumers refused to visit the restaurant for some time after the event.What sample size would be needed in order to be 95% confident that the sample proportion is within 0.02 of p,the true proportion of customers who refuse to go back to the restaurant?

A cable TV company wants to estimate the percentage of people in Alberta watching a particular station during an evening hour.An approximation is 20 percent.They want the estimate to be at the 90 percent confidence level and within 2 percent of the actual proportion.What sample size is needed?

When the population is normally distributed and the population standard deviation $\sigma$ is unknown,then for any sample size n,the confidence interval for $\mu$ is based on the z distribution.

You are studying two normally distributed populations with equal variances.A random sample is taken from each population.The relevant sample statistics are $\bar { x } _ { 1 }$ = 34.36, $\bar { x } _ { 1 }$ = 26.45,s₁ = 9,s₂ = 6,n₁ = 10,n₂ = 16.Compute a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

A sample of 12 items yields an average weight of $\bar { x }$ = 48.5 grams and a standard deviation of s = 1.5 grams.Assuming weights follow a normal distribution,construct a 90 percent confidence interval for the population mean weight.

Consider a normally distributed population.The width of a confidence interval for the population mean will be

You are studying two normally distributed populations with equal variances.A random sample is taken from each population.The relevant sample statistics are $\bar { x } _ { 1 }$ = 64, $\bar { x } _ { 1 }$ = 59, $s _ { 1 } ^ { 2 }$ = 6, $s _ { 2 } ^ { 2 }$ = 3,n₁ = 9,n₂ = 6.Compute a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3cm with a standard deviation of 0.3cm.Assuming bolt length is normally distributed,what is the 99% confidence interval for the true mean length of the bolt?

Consider a normally distributed population with standard deviation 36.If we wish to estimate the population mean to within 10 units with 90% confidence,what is the required sample size?

A new manufacturing method has been introduced to streamline the canning process of cherries.Although the time to fill a can has been reduced,the quality control manager is concerned about the uniformity of the amount of cherries in each can.The manager randomly samples 80 cans over an eight hour shift and obtains a mean cherry content of 14.64 grams.The population standard deviation is known to be 0.4 grams.If cherry content is normally distributed,the 95% confidence interval for the mean cherry content,in grams,is _____.

Consider a normally distribution population with known variance.The width of a 99% confidence interval for the population mean will be _______ the width of a 95% confidence interval for the population mean:

A researcher is investigating the occurrence of traffic tickets in a population.In random sample of 1000 older drivers,275 had traffic tickets within the last year.Of 1000 randomly selected younger drivers,250 had traffic tickets within the last year.Find a 95 percent confidence interval for the difference between the proportions of traffic tickets between older and younger drivers.

In order to decrease the margin of error while everything else is held constant,we must __________ the sample size.

You are studying two normally distributed populations with equal variances.A random sample is taken from each population.The relevant sample statistics are $\bar { x } _ { 1 }$ = 1.94, $\bar { x } _ { 1 }$ = 1.04,s₁ = 0.45,s₂ = 0.26,n₁ = 15,n₂ = 10.Compute a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

A consultant is investigating the defect rates at two widget factories.A random sample of 500 widgets from factory 1 contained 25 defective widgets.Of 2000 randomly selected widgets from factory 2,80 were defective.Find a 90 percent confidence interval for the difference between the proportions of defective widgets in factory 1 and factory 2.

The Ministry of Agriculture tested 105 fuel samples for accuracy of the reported octane level.For premium grade,14 out of 105 samples failed (they didn't meet specifications).How many samples would be needed to create a 95% confidence interval that is within 0.02 of the true proportion of premium grade fuel-quality failures?

At a sobriety checkpoint,the police screened 676 drivers and 6 were arrested for impaired driving.The 92% confidence interval for the true proportion of drivers who were impaired at that time would be _____.

Independent random samples of are taken from each of two normally distributed populations.The relevant sample statistics are n₁ = 10,n₂ = 8, $\bar { x } _ { 1 }$ = 50, $\bar { x } _ { 2 }$ = 42,s₁= 5,and s₂ = 7.If we assume the population variances are equal,give a 95% confidence for $\mu _ { 1 } - \mu _ { 2 }$ )

A coffee shop franchise owner is looking at two possible locations for a new shop. To help make a decision the owner looks at the number of pedestrians that go by each of the two locations in one-hour segments. At location A, counts are taken for 35 one-hour units and with a mean number of pedestrians of 421 and a sample standard deviation of 122. At the second location (B), counts are taken for 50 one hour units with a mean number of pedestrians of 247 and a sample standard deviation of 85. Assume the two populations variances are not known but are equal, and that the number of pedestrians is approximately normal. -Provide a one-sentence interpretation of the 95% confidence interval for the mean difference in pedestrian traffic at the two locations.