According to a study conducted by a statistical​ organization, the proportion of people who are satisfied with the way things are going in their lives is 0.76 . Suppose that a random sample of 100 people is obtained. Complete parts​ (a) through​ (e) below.

​(a) Suppose the random sample of 100 people is​ asked, "Are you satisfied with the way things are going in your​ life?" Is the response to this question qualitative or​ quantitative? Explain.

A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

B. The response is quantitative because the responses can be measured numerically and the values added or​ subtracted, providing meaningful results.

C. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.

D. The response is qualitative because the responses can be measured numerically and the values added or​ subtracted, providing meaningful results.

​(b) Explain why the sample​ proportion, ModifyingAbove p with caret ​, is a random variable. What is the source of the​ variability?

A. The sample proportion ModifyingAbove p with caret is a random variable because the value of ModifyingAbove p with caret represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully.

B. The sample proportion ModifyingAbove p with caret is a random variable because the value of ModifyingAbove p with caret varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully.

C. The sample proportion ModifyingAbove p with caret is a random variable because the value of ModifyingAbove p with caret varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.

D. The sample proportion ModifyingAbove p with caret is a random variable because the value of ModifyingAbove p with caret represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. ​

(c) Describe the sampling distribution of ModifyingAbove p with caret ​, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements. Since the sample size is no ▼ more less than​ 5% of the population size and ​np(1minus ​p)equalsnothinggreater than or equals​10, the distribution of ModifyingAbove p with caret is ▼ skewed right uniform skewed left approximately normal with mu Subscript ModifyingAbove p with caret Baseline equals nothing and sigma Subscript ModifyingAbove p with caret Baseline equals nothing . ​(Round to three decimal places as​ needed.) ​

(d) In the sample obtained in part​ (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.80 ​? The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.80 is nothing . ​(Round to four decimal places as​ needed.)

​(e) Using the distribution from part​ (c), would it be unusual for a survey of 100 people to reveal that 70 or fewer people in the sample are satisfied with their​ lives? The probability that 70 or fewer people in the sample are satisfied is nothing ​, which ▼ (is) or (is not) unusual because this probability ▼ (is not) or (is) less than ▼ (0.05) or (0.5) or (50) or (5) ​%. ​(Round to four decimal places as​ needed.) Click to select your answer(s).

1. The amount of time an alkaline battery lasts is normally distributed with a mean life of
19 hours and standard deviation of 1.2 hours.
(a) 68% of all batteries will last between ____________ hrs. and _____________ hrs.
(b) 95% of all batteries will last between ____________ hrs. and _____________ hrs.
(c) What percent of the batteries will have a life that exceeds 16.6 hours? _________
(d) What percent of the batteries will have a life that lasts between 15.4 and 22.6 hours? ______
(e) If a company purchases 10,000 batteries, how many batteries are expected to last
 more than 17.8 hours? ___________
 between 15.4 and 20.2 hours? ____________

Exercise 9-22 Algo It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 34 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 feet. Assume that the population standard deviation is 22 feet. (You may find it useful to reference the appropriate table: z table or t table)

a. State the null and the alternative hypotheses for the test. H0: μ = 120; HA: μ ≠ 120 H0: μ ≥ 120; HA: μ < 120 H0: μ ≤ 120; HA: μ > 120

b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Find the p-value. p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10

c. Use α = 0.05 to determine if the average breaking distance differs from 120 feet.

An educator claims that the average salary of substitute teachers in school districts in Allegheny County, Pennsylvania, is less than $60 per day. A random sample of eight school districts is selected, and the daily salaries (in dollars) are shown $60   $56 $60   $55   $70 $55 $60   $55. Is there enough evidence to support the educators claim at =0.10?

Group of answer choices

A.P value=0.2765; fail to reject H₀

B.P value=0.2765; reject H₀

C.P value=0.3130; fail to reject H₀

D.P value=0.3130; reject H₀

The mean drying time of a certain paint in a certain application is 12 minutes. A new additive will be tested to see if it reduces the drying time. One hundred specimens will be painted, and the sample mean drying time will be computed. Let μ be the mean drying time for the new paint. Assume the population standard deviation of drying times is 2 minutes. Assume that, in fact, the true mean drying time of the new paint is 11.5 minutes.

a) What are the null and alternative hypotheses?

b) For what values of should Ho be rejected so that the power of the test is .85? What will the level then be?

c) How large of a sample is needed so that a 5% level test has power .85?

An English professor assigns letter grades on a test according to the following scheme.

A: Top 9% of scores

B: Scores below the top 9% and above the bottom 63%

C: Scores below the top 37% and above the bottom 22%

D: Scores below the top 78% and above the bottom 6%

F: Bottom 6% of scores

Scores on the test are normally distributed with a mean of 66.9 and a standard deviation of 9.2. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answer

2 Points

Keypad

Tables

If you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. Note: Selecting a cell will return the value associated with the column and row headers for that cell.

numerical limit 1 and numerical limit 2

A university financial aid office polled a random sample of 528 528 male undergraduate students and 651 651 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 295 295 of the male students and 463 463 of the female students said that they had worked during the previous summer. Give a 80% 80% confidence interval for the difference between the proportions of male and female students who were employed during the summer.

Step 2 of 4 :

Find the critical value that should be used in constructing the confidence interval.

9) (mean) $46 $29 S (Standard Deviation) $ 9 $ 8 Xi (Number of students who are making >$30,000 annually) $10 $ 9 n (Sample Size) 37 26 a) Is there any evidence of a difference in the average between the two groups? H0 ________H1 ________ Graph _________________________, Critical Value(s) ___________Computed Value(s) __________ Decision _____________________________ b) Is there any evidence of a difference in the proportion between the two groups? H0 ________H1 ________ Graph _________________________, Critical Value(s) ___________Computed Value(s) __________ Decision _____________________________

1. Which of the following statements is NOT true about a one-way ANOVA?

2. In a one-way ANOVA, you reject the null hypothesis if your test statistic is larger than the critical value, not if it is smaller than the critical value.

True

False

3. F-ratios can be either positive or negative.

True

False

4. Eta squared tells us how much of the differences between the scores is accounted for by the differences between the groups.

True

False

the statement of the problem:

"Buses arrive at a bus station at a rate 2 buses per minute. the arrival of buses occurs at random times according to a Poisson scatter on (0, infinity). Show all your work for each part."

a. what is the probability that no bus arrives between t = 0 and t = 30 seconds?

b. what is the probability that the third bus arrives after t = 3 minutes?

c. what is the probability that the 5-th bus arrives within 1 minute of the 4-th bus?

d. what is the probability that the 1-st bus arrives in less than 1 minute and fewer than 2 buses arrive between t = 3 and t = 5 minutes.

1) The number of times that student takes an A class, X(X has a line under) has the discrete uniform pmf: p(x) = 0.25 for x = 1,2,3,4. Recall from earlier course material that this pmf has E(X)(X has a line under)=5/2 and V(X)(X has a line under)= 15/12. A random sample of 36 students will be selected and the number of times that have taken A class will be recorded.
-Determine the probability that the mean of this sample is less that 3.

2)The lysine composition is soybean meal was measured in 9 random samples resulting in a sample mean of 22.4 g/kg and standard deviation of 1.2g/kg. Construct a 2-sided 99% confidence interval on the population standard deviation. Assume that the population is normally distributed. What is the estimated of the lower bound of this confidence interval?

Information on a large packet of seeds indicates that the germination rate is p0=92%. Some researchers claim that the proportion of germination should be higher than that.

(a) (2 points) Based on the indication of the information, what’s the probability that more than 95% of the 300 seeds in the packet will germinate?
(b) (3 points) Now a random sample containing 300 seeds with 290 germinated is chosen to test this claim. Based on the sample, construct a 90% confidence interval for the population proportion of the seeds germinated in one packet. Please interpret the interval.
(c) (5 points) If some researchers want to conduct a large-scale study, hoping to estimate the proportion to within 1% with 98% confidence, how many seeds must contain in the sample?

STUDY 4

The university is building a number of active learning classrooms and came across a chair called the Ruckus Stool that is designed specifically for collaborative work. The design allows users to comfortably use it frontward and backwards, but you are unsure whether it will work for a wide range of activities. To test the design before ordering a large number, you ask a group of students to try it for three types of lessons: i) lecture, ii) two-person group work, iii) four-person group work. Each student only tries a single lesson type. You ask each student to record the number of times they had to adjust their seating position due to physical discomfort. You are interested in whether the lesson type impacts comfort in this chair.

i. Identify and rationalize the most appropriate statistical test.

ii. State the null and alternative hypothesis for the question whether there is an effect of lesson type.

iii. Identify the appropriate test statistic.

Question 5 options:

Question 6 (3 points)

For each of the following studies, identify and rationalize the most appropriate statistical test (e.g., t-test, regression etc.). Include the null and alternative hypotheses (be mindful of direction in the test), as well as the appropriate test statistic (e.g., F-score for an F-test).

STUDY 2

A geneticist was interested in the degree to which behavior is determined by gender. She conducted a survey of 40 random students. The scientist categorized each student as being male or female, and their study behavior as diligent, procrastination or reactive. She wants to know whether study style depends on gender.

i. Identify and rationalize the most appropriate statistical test.

ii. State the null and alternative hypotheses in terms of the relationship between the variables.

iii. Identify the appropriate test statistic.

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 13 13 students, taught in traditional lab sessions, had a mean test score of 74.8 74.8 with a standard deviation of 4.3 4.3 . A random sample of 19 19 students, taught using interactive simulation software, had a mean test score of 87.3 87.3 with a standard deviation of 5.6 5.6 . Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ1 μ 1 be the mean test score for the students taught in traditional lab sessions and μ2 μ 2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.05 α = 0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 4 : State the null and alternative hypotheses for the test.

Can u post all 4 steps ?

Nine homes are chosen at random from real estate listings in two suburban neighborhoods, and the square footage of each home is noted in the following table.

(a) Choose the appropriate hypothesis to test if there is a difference between the average sizes of homes in the two neighborhoods at the .10 significance level. Assume μ₁ is the mean of home sizes in Greenwood and μ₂ is the mean of home sizes in Pinewood.

(c) Find the test statistic t_calc. (A negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

(d) Assume unequal variances to find the p-value. (Use the quick rule to determine degrees of freedom. Round your answer to 4 decimal places.)