stats final

There are 28 different colored pencils in a box. What is the probability that the orange pencil and then the green pencil will be chosen at random, without replacement? Enter a fraction or round your answer to 4 decimal places, if necessary.

0.0013

Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.5 years with a standard deviation of 0.8 years. Step 1 of 2: If a sampling distribution is created using samples of the ages at which 44 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.

5.5

The National Academy of Science reported that 31% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 31 % . He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 296 recent articles published by reputable mathematics research journals and finds that 71 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 31 % ? Use a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below.

not equal

Identify the sampling technique used for the following study. After a quality assurance analyst has assigned identification numbers to a population, she picks a random starting point and chooses every fiftieth member.

systematic sampling

A recent survey reported that small businesses spend 30 hours a week marketing their business. A local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 30 hours a week on marketing. The chamber conducts a survey of 80 small businesses within their state and finds that the average amount of time spent on marketing is 28.9 hours a week. Assuming that the population standard deviation is 6.5 hours, is there sufficient evidence to support the chamber of commerce's claim at the 0.05 level of significance? Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.

-1.51

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 211 cars owned by students had an average age of 6.88 years. A sample of 253 cars owned by faculty had an average age of 8.48 years. Assume that the population standard deviation for cars owned by students is 3.35 years, while the population standard deviation for cars owned by faculty is 3.38 years. Determine the 80 % confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 1 of 3: Find the point estimate for the true difference between the population means.

-1.6

The National Academy of Science reported that 31% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 31 % . He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 296 recent articles published by reputable mathematics research journals and finds that 71 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 31 % ? Use a 0.05 level of significance. Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.

-2.61

A real estate agent has 19 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling no more than 3 properties in one week. Round your answer to four decimal places.

0.0022

Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.5 years with a standard deviation of 0.8 years. Step 2 of 2: If a sampling distribution is created using samples of the ages at which 44 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

0.12

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50 % of this population prefers the color red. If 18 buyers are randomly selected, what is the probability that exactly 7 buyers would prefer red? Round your answer to four decimal places.

0.1214

A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there were 2287 class attendees. The data is summarized in the table below.

0.2331

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.4 and a mean diameter of 212 inches. If 80 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be less than 211.9 inches? Round your answer to four decimal places.

0.2611

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 211 cars owned by students had an average age of 6.88 years. A sample of 253 cars owned by faculty had an average age of 8.48 years. Assume that the population standard deviation for cars owned by students is 3.35 years, while the population standard deviation for cars owned by faculty is 3.38 years. Determine the 80 % confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 2 of 3: Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

0.403159

The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the standard deviation of the waiting time is 2 minutes. Find the probability that a person will wait for between 2 and 7 minutes. Round your answer to four decimal places.

0.6687

The life of light bulls is distributed normally. The standard deviation of the lifetime is 30 hours and the mean lifetime of a bull is 520 hours. Find the probability of a bull lasting for at most 544 hours. Round your answer to four decimal places.

0.7881

The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.14 kWh. A previous study found that for an average family the variance is 1.69 kWh and the mean is 15.9 kWh per day. If they are using a 80 % level of confidence, how large of a sample is required to estimate the mean usage of electricity? Round your answer up to the next integer.

142

Suppose ACT Composite scores are normally distributed with a mean of 21.2 and a standard deviation of 5.4. A university plans to admit students whose scores are in the top 45%. What is the minimum score required for admission? Round your answer to the nearest tenth, if necessary.

21.9

Sarah believes that completely cutting caffeine out of a person's diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah's claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. test statistic

3.274 / reject the null

Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 18. Using the empirical rule, what percentage of 1Q scores are between 50 and 158?

99.7%

A recent survey reported that small businesses spend 30 hours a week marketing their business. A local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 30 hours a week on marketing. The chamber conducts a survey of 80 small businesses within their state and finds that the average amount of time spent on marketing is 28.9 hours a week. Assuming that the population standard deviation is 6.5 hours, is there sufficient evidence to support the chamber of commerce's claim at the 0.05 level of significance? Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below.

<

Sarah believes that completely cutting caffeine out of a person's diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah's claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2.

>

what is the population? The heights of 14 out of the 25 tomato plants at Mr. Lonardo's greenhouse.

All tomato plants at Mr. Lonardo's greenhouse.

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 211 cars owned by students had an average age of 6.88 years. A sample of 253 cars owned by faculty had an average age of 8.48 years. Assume that the population standard deviation for cars owned by students is 3.35 years, while the population standard deviation for cars owned by faculty is 3.38 years. Determine the 80 % confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 3 of 3: Construct the 80 % confidence interval. Round your answers to two decimal places.

Lower endpoint: -2.00 Upper endpoint: -1.20

In a random sample of 25 residents of the state of New Hampshire, the mean waste recycled per person per day was 1.0 pounds with a standard deviation of 0.58 pounds. Determine the 98% confidence interval for the mean waste recycled per person per day for the population of New Hampshire. Assume the population is approximately normal. Round your answer to one decimal place.

Lower endpoint: 0.7 Upper endpoint: 1.3

identify the sample The types of cars of a sample of 26 parents of your classmates.

The 26 parents of your classmates.

A recent survey reported that small businesses spend 30 hours a week marketing their business. A local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 30 hours a week on marketing. The chamber conducts a survey of 80 small businesses within their state and finds that the average amount of time spent on marketing is 28.9 hours a week. Assuming that the population standard deviation is 6.5 hours, is there sufficient evidence to support the chamber of commerce's claim at the 0.05 level of significance? Step 3 of 3: Draw a conclusion and interpret the decision.

We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the chamber's claim that businesses are spending less than 30 hours a week on marketing.

The National Academy of Science reported that 31% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 31 % . He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 296 recent articles published by reputable mathematics research journals and finds that 71 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 31% ? Use a 0.05 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision.

We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the percentage of research in mathematics published by US authors has changed.

Lengths of time it takes for new light bulbs to burn out are an example of which type of data?

continuous

IQ scores, reported in whole numbers, of research scientists are an example of which type of data?

discrete