A journal published a study of the lifestyles of visually impaired students. Using​ diaries, the students kept track of several​ variables, including number of hours of sleep obtained in a typical day. These visually impaired students had a mean of 9.06hours and a standard deviation of 2.11 hours. Assume that the distribution of the number of hours of sleep for this group of students is approximately normal. Complete parts a through c.

A. Find P(x<6)

b. Find P(8≤x≤10)

c. Find the value a for which P(x<a)= 0.3

A researcher at the Annenberg School of Communication is interested in studying the use of smartphones among young adults. She wants to know the average amount of time that college students in the United States hold a smartphone in their hand each day. The researcher obtains data for one day from a random sample of 25 college students (who own smartphones). She installs an app that registers whenever the smartphone is being held and the screen is on. The sample mean is 230 minutes, with a standard deviation of 11 minutes.

What is the 99% confidence interval for average daily time a smartphone is used among college students?

What is the lower bound of the confidence interval?   

What is the upper bound of the confidence interval?

What decision should the researcher make about the null hypothesis? Be sure to explain your answer (e.g., what numbers provide the basis for this decision?).

Would our decision about the null hypothesis have been different if the researcher had initially hypothesized that women spend more time talking on their phones than men?

Explain all parts/information necessary to answer this question.

A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 19% were under 20 years old, 13% were in the 20- to 35-year-old bracket, 30% were between 36 and 50, 24% were between 51 and 65, and 14% were over 65. A study done this year used a random sample of 210 residents. This sample is given below. At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: Time ten years ago and today are independent.
H₁: Time ten years ago and today are not independent.H₀: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are independent.
H₁: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are not independent.    H₀: The population 10 years ago and the population today are independent.
H₁: The population 10 years ago and the population today are not independent.H₀: The distributions for the population 10 years ago and the population today are the same.
H₁: The distributions for the population 10 years ago and the population today are different.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)


(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(iv) Conclude the test.

Since the P-value < α, we reject the null hypothesis.Since the P-value ≥ α, we do not reject the null hypothesis.    Since the P-value ≥ α, we reject the null hypothesis.Since the P-value < α, we do not reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to claim that the age distribution of the population of Blue Valley has changed.At the 1% level of significance, there is sufficient evidence to claim that the age distribution of the population of Blue Valley has changed.    

A researcher wishes to​ estimate, with 99​% confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 55​% of the population proportion.

​(a) No preliminary estimate is available. Find the minimum sample size needed.

​(b) Find the minimum sample size​ needed, using a prior study that found that 42​% of the respondents said they eat fast food four to six times per week.

​(c) Compare the results from parts​ (a) and​ (b).

​(a) What is the minimum sample size needed assuming that no prior information is​ available?

Please answer all the questions.

which type of English word is longer:nouns, verbs or adjectives? Go to a book of at least 400 pages and turn to a random pages using the random numbers listed at the end of this paragraph. Go down the page until you come to a noun. Note its length (in a number of letters). Do this for 10 different nouns. Do the same for every 10 verbs and for 10 adjectives. Using .05 significance level, a) carry out an analysis of variance comparing the three types of words, b) figure a planned contrast of nouns versus verbs.

73, 320, 179, 323, 219, 176, 167, 102, 228, 352, 4, 335, 118, 12, 333, 123, 38, 49, 399, 17, 188, 264, 342, 89, 13, 77, 378, 223, 92, 77, 378, 223, 92, 77, 152, 34, 214, 754, 83, 198, 210

Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 5,650 pounds and the standard deviation is 240 pounds. Assume that the population follows the normal distribution. Forty-five trucks are randomly selected and weighed.

Within what limits will 90% of the sample means occur? (Round your z-value to 2 decimal places and final answers to 1 decimal place.)

Sample means _______ to _______

The makers of a child's swing set claim that the average assembly time is less than 2 hours. A sample of 35 assembly times (in hours) for this swing set is given in the table below. Test their claim at the 0.10 significance level. (a) What type of test is this? This is a right-tailed test. This is a two-tailed test. This is a left-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. t x = (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0 (e) Choose the appropriate concluding statement. The data supports the claim that the mean assembly time is less than 2 hours. There is not enough data to support the claim that the mean assembly time is less than 2 hours. We reject the claim that the mean assembly time is less than 2 hours. We have proven that that the mean assembly time is less than 2 hours. DATA ( n = 35 ) Assembly Time Hours 1.00 2.51 1.31 1.98 1.93 2.25 0.94 2.10 1.27 2.71 3.18 1.76 1.50 2.75 0.77 0.63 2.31 0.11 1.31 1.92 2.40 2.04 1.53 0.76 1.04 2.37 2.38 1.35 3.55 1.29 1.68 2.23 0.64 2.34 2.41

A small community college claims that their average class size is equal to 35 students. This claim is being tested with a level of significance equal to 0.02 using the following sample of class sizes: 42, 28, 36, 47, 35, 41, 33, 30, 39, and 48. Assume class sizes are normally distributed. (NOTE: We need to assume that class sizes are normally distributed in order to use the t distribution because the sample size n=10 < 25, and the Central Limit Theorem does not apply.)

Which of the following conclusions can be drawn?

• A.

  Since the test statistic equals 1.36, fail to reject the null hypothesis and conclude that there's insufficient evidence to conclude that class size does not equal 35 students.

• B.

  Since the test statistic equals 2.26, fail to reject the null hypothesis and conclude that class size does equal 35 students.

• C.

  Since the test statistic equals 2.05, reject the null hypothesis and conclude that class size does not equal 35 students.

• D.

  Since the test statistic equals 1.58, reject the null hypothesis and conclude that class size does not equal 35 students.

In a survey of 3992 adults, 717 oppose allowing transgender students to use the bathrooms of the opposite biological sex. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

A​ 99% confidence interval for the population proportion is (,)

1. According to a study, 20% of corporate officers at public-held companies are women. Suppose that you select a random sample of 250 corporate officers.
   1. What is the probability that in the sample, less than 15% of the corporate officers will be women?
   2. What is the probability that in the sample, between 13% and 17% of the corporate officers will be women?
   3. What is the probability that in the sample between 10% and 20% of the corporate officers will be women?

Question text

In the early 1990's, the Oregon Department of Education was looking into the success of their school lunch programs. Critics of the current way funds were being diverted to school food services believed that the low quality of the food being served in the low-income school districts was leading to malnutrition among the students.

The state had already collected growth data for decades throughout Oregon, so they went through their records to look for signs of malnutrition. One metric they used was heights of children in the various school districts. If children did not have proper nutrition from healthy food, they would not grow to their full potential.

The CDC/National Center for Health Statistics put the average height for 12 year old girls in the United States at 59.4 inches, with standard deviation 2.3 inches.

1. Assume that heights are normally distributed. If we randomly selected a 12-year-old female student in a local school, what is the probability that she is no more than 55.4 inches tall?  

The Klamath county school district reported that their female 12-year-old students had a mean height of 58.2 inches out of a sample of 27 students. This a little more than an inch below the population mean for all 12 year old girl's heights.

2. Let's define an unusual event to be one where the probability of it occurring is less than 0.05 (or, equivalently, less than 1 in 20). If we wanted to find out if the school district's mean height was unusually low, what probability should we find?

(Hint: if 58 inches tall is unusually low, then so is 57 inches, and 56 inches.... )

Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force whose job it is to call on existing customers as well as look for new business. The national sales manager is investigating the relationship between the number of sales calls made and the miles driven by the sales representative. Also, do the sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions? To investigate, the vice president of sales selected a sample of 25 sales representatives and determined:

The amount earned in commissions last month (Y).

The number of miles driven last month (X1)

The number of sales calls made last month (X2)

Click here for the Excel Data File

Develop a regression equation including an interaction term. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

A.) Commissions =_______ +________ Calls +________ Miles +______ X1X2

B.) Complete the following table. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

Predictor Coefficient    SE Coefficient    T P-value

Constant _______         __________    ___   _________

Calls

Miles

X1X2

C.) Compute the value of the test statistic corresponding to the interaction term. (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

Five people, including you and a friend, line up at random. The random variable X denotes the number of people between yourself and your friend. Use R to show this distribution in a graph.

A) A company that manufactures oil seals found the population mean to be 49.15 mm (1.935 in.), the pop- ulation standard deviation to be 0.51 mm (0.020 in.), and the data to be normally distributed. If the internal diameter of the seal is below the lower specification limit of 47.80 mm, the part is reworked. However, if it is above the upper specification limit of 49.80 mm, the seal is scrapped.

(a) What percentage of the seals is reworked? What percentage is scrapped?

(b) For various reasons, the process average is changed to 48.50 mm. With this new mean or process center, what percentage of the seals is reworked? What percentage is scrapped? If rework is economically feasible, is the change in the process center a wise decision?