An agency conducted a car crash test of booster seats for cars. The results of the tests are given, with the units being hic (standard head injury condition units). Calculate and interpret 95% confidence interval for the true mean measurement. You can assume its a normal population of measurements. Please show work. 774 649 1210 546 431 612

Exercise 15-6 Algo

When estimating a multiple linear regression model based on 30 observations, the following results were obtained. [You may find it useful to reference the t table.]

a-1. Choose the hypotheses to determine whether x₁ and y are linearly related.

• H₀: β₁ = 0; H_A: β₁ ≠ 0

• H₀: β₀ = 0; H_A: β₀ ≠ 0

• H₀: β₀ ≤ 0; H_A: β₀ > 0

• H₀: β₁ ≤ 0; H_A: β₁ > 0

a-2. At the 5% significance level, when determining whether x₁ and y are linearly related, the decision is to:

• Reject H₀x₁ and y are linearly related.
• Reject H₀x₁ and y are not linearly related.
• Do not reject H₀we cannot conclude x₁ and y are linearly related.

b-1. What is the 95% confidence interval for β₂? (Negative values should be indicated by a minus sign. Round "t_α/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

b-2. Using this confidence interval, is x₂ significant in explaining y?

• No, since the interval does not contain zero.

• No, since the interval contains zero.

• Yes, since the interval does not contain zero.

• Yes, since the interval contains zero.

c-1. At the 5% significance level, choose the hypotheses to determine if β₁ is less than 20.

• H₀: β₁ ≥ 20; H_A: β₁ < 20

• H₀: β₁ ≤ 20; H_A: β₁ > 20

• H₀: β₁ = 20; H_A: β₁ ≠ 20

c-2. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

c-3. At the 5% significance level, can you conclude that β₁ is less than 20?

• Yes, since the null hypothesis is rejected.

• Yes, since the null hypothesis is not rejected.

• No, since the null hypothesis is not rejected.

• No, since the null hypothesis is rejected.

A real estate analyst estimates the following regression, relating a house price to its square footage (Sqft):

PriceˆPrice^ = 48.21 + 52.11Sqft; SSE = 56,590; n = 50

In an attempt to improve the results, he adds two more explanatory variables: the number of bedrooms (Beds) and the number of bathrooms (Baths). The estimated regression equation is

PriceˆPrice^ = 28.78 + 40.26Sqft + 10.70Beds + 16.54Baths; SSE = 48,417; n = 50

[You may find it useful to reference the F table.]

a. Choose the appropriate hypotheses to determine whether Beds and Baths are jointly significant in explaining Price.

• H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is nonzero.

• H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is greater than zero.

• H₀: β₁ = β₂ = β₃ = 0; H_A: At least one of the coefficients is nonzero.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

• p-value < 0.01

• p-value 0.10
• 0.05 p-value < 0.10

c. At the 5% significance level, what is the conclusion to the test?

• Reject H₀Beds and Baths are jointly significant in explaining Price.
• Reject H₀Sqft Beds and Baths are jointly significant in explaining Price.
• Do not reject H₀Sqft Beds and Baths are not jointly significant in explaining Price.
• Do not reject H₀Beds and Baths are not jointly significant in explaining Price.

rev: 06_11_2019_QC_CS-170121

Let A , B , and C be disjoint subsets of the sample space. For each one of the following statements, determine whether it is true or false. Note: "False" means "not guaranteed to be true."

a) P(A)+P(Ac)+P(B)=P(A∪Ac∪B)

b) P(A)+P(B)≤1

c) P(Ac)+P(B)≤1

d) P(A∪B∪C)≥P(A∪B)

e) P((A∩B)∪(C∩Ac))≤P(A∪B∪C)P((A∩B)∪(C∩Ac))≤P(A∪B∪C)

f) P(A∪B∪C)=P(A∩Cc)+P(C)+P(B∩Ac∩Cc)

)

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours. Language Spanish French German System 1 7 10 15 11 14 19 System 2 6 14 16 10 16 22 Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use . Complete the following ANOVA table (to 2 decimals, if necessary). Round your p-value to 4 decimal places.

1. Here are summary statistics for randomly selected weights of newborn girls: n=159, x=28.8 hg, s=7.7 hg.Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 26.6 hg<u<32.0 hg with only 13 sample values, x=29m3 hg, and s= 3.6 hg?

What is the confidence interval for the population mean u?

__ hg<u<___ hg

2. A data set includes 109 body temperatures of healthy adult humans having a mean of 98.3 F and a standard deviation of 0.54 F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the mean suggest about the use of 98.6 F as the mean body temperature?
What is the confidence interval estimate of the population mean u?

___F<u<____F

3.In a test of the effectiveness of garlic for lowering cholesterol, 48 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in ther levels of LDL cholesterol (in mg/dL) have a mean of 4.4 and a standard deviation of 15.9. Construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
What is the confidence interval estimate of the population mean u?

__mg/dL<u<___mg/dL

Given the data below, a lower specification of 78.2, and an upper specification of 98.9, what is the long term process performance (Ppk)?

Data
101.4791
94.02297
95.41277
106.7218
90.35416
86.9332
94.87044
95.91265
93.98042
108.558
86.17921
85.01441
96.14778
92.59247
92.49536
87.4595
104.3463
90.57274
99.38992
80.61536
82.31772
97.05331
87.64293
103.3648
98.09292
87.72921
110.1765
86.76847
87.22422
94.88148
86.01183
91.43283
104.0907
97.77132
98.69138
95.55565
106.2402
95.96255
88.05735
100.2796
99.00995
86.18458
95.41366
99.32314
95.75733
88.82675
93.39986
98.34077
94.72198
99.14256
92.37767
94.94969
89.63531
87.56148
88.02731
97.57498
98.4039
98.18642
102.5057
88.69717
90.61504
87.80989
102.4578
92.72643
96.0759
92.81471
86.44152
101.1881
92.64199
84.96657
96.75944
94.76492
86.555
91.5101
97.21423
92.36803
90.68739
88.16595
94.48869
87.61221
101.9311
98.71314
109.3335
97.20268
88.36405
90.59582
89.18839
95.28564
99.59782
92.92415
96.54786
96.07842
93.63263
107.0558
93.20436

When estimating a multiple linear regression model based on 30 observations, the following results were obtained. [You may find it useful to reference the t table.]

a-1. Choose the hypotheses to determine whether x₁ and y are linearly related.

• H₀: β₀ ≤ 0; H_A: β₀ > 0

• H₀: β₁ ≤ 0; H_A: β₁ > 0

• H₀: β₀ = 0; H_A: β₀ ≠ 0

• H₀: β₁ = 0; H_A: β₁ ≠ 0

a-2. At the 5% significance level, when determining whether x₁ and y are linearly related, the decision is to:

• Reject H₀x₁ and y are linearly related.
• Reject H₀x₁ and y are not linearly related.
• Do not reject H₀we cannot conclude x₁ and y are linearly related.

b-1. What is the 95% confidence interval for β₂? (Negative values should be indicated by a minus sign. Round "t_α/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

b-2. Using this confidence interval, is x₂ significant in explaining y?

• No, since the interval does not contain zero.

• No, since the interval contains zero.

• Yes, since the interval does not contain zero.

• Yes, since the interval contains zero.

c-1. At the 5% significance level, choose the hypotheses to determine if β₁ is less than 20.

• H₀: β₁ ≤ 20; H_A: β₁ > 20

• H₀: β₁ ≥ 20; H_A: β₁ < 20

• H₀: β₁ = 20; H_A: β₁ ≠ 20

c-2. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

c-3. At the 5% significance level, can you conclude that β₁ is less than 20?

• Yes, since the null hypothesis is rejected.

• Yes, since the null hypothesis is not rejected.

• No, since the null hypothesis is not rejected.

• No, since the null hypothesis is rejected.

A real estate analyst estimates the following regression, relating a house price to its square footage (Sqft):

PriceˆPrice^ = 48.36 + 52.50Sqft; SSE = 56,018; n = 50

In an attempt to improve the results, he adds two more explanatory variables: the number of bedrooms (Beds) and the number of bathrooms (Baths). The estimated regression equation is

PriceˆPrice^ = 28.71 + 40.44Sqft + 10.58Beds + 16.44Baths; SSE = 48,937; n = 50

[You may find it useful to reference the F table.]

a. Choose the appropriate hypotheses to determine whether Beds and Baths are jointly significant in explaining Price.

• H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is greater than zero.

• H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is nonzero.

• H₀: β₁ = β₂ = β₃ = 0; H_A: At least one of the coefficients is nonzero.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

• 0.025p-value < 0.05
• 0.01p-value < 0.025

• p-value < 0.01

• p-value0.10
• 0.05p-value < 0.10

c. At the 5% significance level, what is the conclusion to the test?

• Reject H₀Beds and Baths are jointly significant in explaining Price.
• Reject H₀Sqft Beds and Baths are jointly significant in explaining Price.
• Do not reject H₀ SqftBeds and Baths are not jointly significant in explaining Price.
• Do not reject H₀Beds and Baths are not jointly significant in explaining Price.

A community centre is going to hold a yaga class with 15 regisitered students. From the previous report of Yoga class, the absent rate per students is 5%. i) Calculate the probability that at most 13 students will attend the yoga class.

The Tvet college is interested in the relationship between anxiety level and the need to succeed in school. A random sample of 400 students took a test that measured anxiety level and need to succeed in school. Need to succeed in school vs Anxiety level Need to succeed High Med–High Medium Med–Low Low in school Anxiety Anxiety Anxiety Anxiety Anxiety High Need 35 42 53 15 10 Medium Need 18 48 63 33 31 Low Need 4 5 11 15 17 Which one of the following statements is incorrect?
1. The column total for a high anxiety level is 57:
2. The row total for high need to succeed in school is 155:
3. The expected number of students who have a high anxiety level and a high need to succeed in school is about 51:
4. The expected number of students who have a low need to succeed in school and a med–low level of anxiety is 8:19:
5. The expected number of students who have a medium need to succeed in school and a medium anxiety is 61:28:

the critical value of 2 at 10% significance level equals.
1. 17:535
2. 13:362
3. 20:090
4. 2:733
5. 15:98

1.The gasoline consumption of an engine has a normal distribution with mean 5 gallons. In four independent tests, the probability that the average gasoline consumption is over 5 gallons is

A.none of these

B.0.50

C.1

D.0

2.Time (in minute) spent using e-mail per session is normally distributed with a mean of 4.5 minutes. Let P be the probability that the sample mean in a random sample of 25 sessions is between 4 minutes and 5 minutes. Let Q be the probability that the sample mean in a random sample of 64 sessions is between 4 minutes and 5 minutes. Then,

A.none of these is correct

B.P < Q

C.P > Q

D.P = Q

3.The central limit theorem states that as sample size gets large enough,

A.the distribution of the population data values becomes the normal distribution

B.the distribution of the sample data values becomes the normal distribution

C.the sampling distribution of the population mean becomes the normal distribution

D.the sampling distribution of the sample mean becomes the normal distribution

4.For a sample of size 2 or above, which of the following statements about sample mean are true?

I. Both population mean and sample mean are random variables.

II. The population mean and the expected value of the sample mean are the same.

III. The population standard deviation of is larger than the standard deviation of the sample mean.

A.I and III

B.I, II and III

C.II and III

D.I and II

Are U-Albany students more likely to approve gun control than adults in the U.S.? According to a research report, on a scale from 1 to 10, the mean approval of gun control in the U.S. is 7.8. The mean approval of gun control in a random sample of 26 U-Albany students is 8.3, with the standard deviation of 2.2. Use α = 0.01 for the hypothesis testing. Questions 28 to 32 are based on this example.
28. What would be the H0 for the example?
A. U-Albany students are equally likely to approve gun control than adults in the U.S.
B. The likelihood of approving gun control among U-Albany students is different from that of the U.S. adults.
C. There is no difference between the 26 U-Albany students and all U.S. adults in terms of their attitudes toward gun control.
D. U-Albany students are less likely to approve gun control than adults in the U.S.

29. What would be the t critical value(s)?

30. What’s the standard error based on the sample information?

31. What is the t obtained value?

32. What conclusion can we make for this example?
A. We cannot reject the null hypothesis that the mean approval of gun control among the 26 U-Albany students is 8.3.
B. There is no enough evidence to reject the null hypothesis that the mean approval of gun control among U-Albany students is 8.3.
C. We cannot reject the null hypothesis that the mean approval of gun control among all U-Albany students is 7.8.
D. We can reject H0 and accept H1 that the mean approval of gun control among all U-Albany students is larger than 7.8.