Exam 7: Sampling Distributions

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine. -The sampling distribution of the sample mean will be approximately normal only if the population sampled is normal.

Instruction 7.4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. -Referring to Instruction 7.4,what is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site?

As the sample size increases,the standard error of the mean increases.

Sales prices of matchbox cars from the 1960s are known to possess a skewed-right distribution with a mean sale price of $5.25 and a standard deviation of $2.80.Suppose a random sample of 100 cars from the 1960s is selected.Describe the sampling distribution for the sample mean sale price of the selected cars.

If the amount of petrol purchased per car at a large petrol station has a population mean of $15 and a population standard deviation of $4 and it is assumed that the amount of petrol purchased per car is symmetric,there is approximately a 68.26% chance that a random sample of 16 cars will have a sample mean between $14 and $16.

If the amount of petrol purchased per car at a large petrol station has a population mean of $15 and a population standard deviation of $4 and a random sample of 4 cars is selected,there is approximately a 68.26% chance that the sample mean will be between $13 and $17.

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. -Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be greater than 88 minutes is __________.

Instruction 7.1 Times spent studying by students in the week before final exams follow a normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. -Referring to Instruction 7.1,what is the probability that the sample mean is more than 3 hours below the population mean?

Sampling error can be completely eliminated by taking larger sample sizes.

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

The Central Limit Theorem is important in statistics because

For distributions such as the normal distribution,the arithmetic mean is considered more stable from sample to sample than other measures of central tendency.

Instruction 7.6 Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. -Referring to Instruction 7.6,90% of the samples proportions symmetrically around the population proportion will have between _________ % and _________ % of the customers who take advantage of online customer service.

Instruction 7.4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. -Referring to Instruction 7.4,what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

Instruction 7.4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. -Referring to Instruction 7.4,what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

Instruction 7.3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. -Referring to Instruction 7.3,the probability is 0.15 that the sample mean lifetime is more than how many hours?

The Central Limit Theorem allows one to make inferences about the population mean but requires that one knows the specific shape of the population distribution.

Instruction 7.5 According to an article, 19% of the entire Australian population have high-speed access to the Internet. Random samples of size 200 are selected from the Australian population. -Referring to Instruction 7.5,among all the random samples of size 200,90% will have more than _________ % who have high-speed access to the Internet.

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. -Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be less than 82 minutes is _______

In inferential statistics,the standard error of the sample mean assesses the uncertainty or error of estimation.