Question

for these questions I need help on just the questions on all of them where it says "what is the value of the sample test statistic?"

24.) The average annual miles driven per vehicle in the United States is 11.1 thousand miles, with σ ≈ 600 miles. Suppose that a random sample of 36 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.9thousand miles. Does this indicate that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average? Use a 0.05 level of significance.

What are we testing in this problem?

single meansingle proportion   

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 11.1; H₁:  μ < 11.1H₀: μ = 11.1; H₁:  μ > 11.1     H₀: p = 11.1; H₁:  p > 11.1H₀: p = 11.1; H₁:  p < 11.1H₀: μ = 11.1; H₁:  μ ≠ 11.1H₀: p = 11.1; H₁:  p ≠ 11.1

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ.     The Student's t, since we assume that x has a normal distribution with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

25.) Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 79 students shows that 37 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance.

What are we testing in this problem?

single meansingle proportion   

(a) What is the level of significance?
  

State the null and alternate hypotheses.

H₀: p = 0.35; H₁:  p < 0.35H₀: p = 0.35; H₁:  p ≠ 0.35     H₀: μ = 0.35; H₁:  μ < 0.35H₀: μ = 0.35; H₁:  μ ≠ 0.35H₀: p = 0.35; H₁: p > 0.35H₀: μ = 0.35; H₁: μ > 0.35

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since np > 5 and nq > 5.The standard normal, since np > 5 and nq > 5.     The standard normal, since np < 5 and nq < 5.The Student's t, since np < 5 and nq < 5

What is the value of the sample test statistic? (Round your answer to two decimal places.)

26.) The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.32 A, with a sample standard deviation of s = 0.44 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)

What are we testing in this problem?

single proportionsingle mean   

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 0.8; H₁:  μ > 0.8H₀: μ ≠ 0.8; H₁:  μ = 0.8     H₀: p = 0.8; H₁:  p ≠ 0.8H₀: p = 0.8; H₁:  p > 0.8H₀: μ = 0.8; H₁:  μ ≠ 0.8H₀: p ≠ 0.8; H₁:  p = 0.8

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since we assume that x has a normal distribution with unknown σ.     The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

27.) A hospital reported that the normal death rate for patients with extensive burns (more than 40% of skin area) has been significantly reduced by the use of new fluid plasma compresses. Before the new treatment, the mortality rate for extensive burn patients was about 60%. Using the new compresses, the hospital found that only 45 of 95 patients with extensive burns died. Use a 1% level of significance to test the claim that the mortality rate has dropped.

What are we testing in this problem?

single proportionsingle mean

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.6; H₁:  p < 0.6H₀: μ = 0.6; H₁:  μ < 0.6     H₀: p = 0.6; H₁: p > 0.6H₀: μ = 0.6; H₁:  μ ≠ 0.6H₀: μ = 0.6; H₁: μ > 0.6H₀: p = 0.6; H₁:  p ≠ 0.6

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal, since np < 5 and nq < 5.The Student's t, since np > 5 and nq > 5.     The Student's t, since np < 5 and nq < 5.The standard normal, since np > 5 and nq > 5

What is the value of the sample test statistic? (Round your answer to two decimal places.)

28.)The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 8. A random sample of 96 matchboxes shows the average number of matches per box to be 42.9. Using a 1% level of significance, can you say that the average number of matches per box is more than 40?

What are we testing in this problem?

single proportionsingle mean

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: p = 40; H₁:  p ≠ 40H₀: μ = 40; H₁:  μ < 40     H₀: p = 40; H₁:  p > 40H₀: p = 40; H₁:  p < 40H₀: μ = 40; H₁:  μ > 40H₀: μ = 40; H₁:  μ ≠ 40

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.     The standard normal, since we assume that x has a normal distribution with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

29.) The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journal). A random sample of 119 employees in the private sector showed that 32 have a bachelor's degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector? Use α = 0.05.

What are we testing in this problem?

single meansingle proportion   

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 0.36; H₁: μ > 0.36H₀: μ = 0.36; H₁: μ ≠ 0.36     H₀: p = 0.36; H₁:  p ≠ 0.36H₀: p = 0.36; H₁:  p < 0.36H₀: μ = 0.36; H₁:  μ < 0.36H₀: p = 0.36; H₁: p > 0.36

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since np > 5 and nq > 5.The standard normal, since np > 5 and nq > 5.     The standard normal, since np < 5 and nq < 5.The Student's t, since np < 5 and nq < 5

What is the value of the sample test statistic? (Round your answer to two decimal places.)

31.) The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the time of replacement were (in months):

21

42

49

48

53

46

30

51

42

52

(i) Use your calculator to calculate the mean age of a car when the fuel injection system fails x and standard deviation s. (Round your answers to two decimal places.)

(ii) Test the claim that the fuel injection system lasts less than an average of 48 months before needing replacement. Use a 5% level of significance.

What are we testing in this problem?

single proportionsingle mean

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 48; H₁:  μ > 48H₀: p = 48; H₁:  p ≠ 48     H₀: μ = 48; H₁:  μ < 48H₀: p = 48; H₁:  p < 48H₀: p = 48; H₁:  p > 48H₀: μ = 48; H₁:  μ ≠ 48

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.     The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Answer 1

24) The test statistic is

// 11 –

10900 – 11100 600/736

= -2.00

25) $\widehat p$ = 37/79 = 0.4684

The test statistic is

p - p p(1-P)

  

10.4684 -0.35 v 0.35(1-0.35) 79

= 2.21

26) The test statistic is

α – s/ μ n

  

1.32 - 0.8 0.44/19

= 3.545

27) $\widehat p$ = 45/95 = 0.474

The test statistic is

p - p p(1-P)

  

0.474 -0.6 0.6(1-0.6) 95

= -2.51

28) The test statistic is

// 11 –

42.9 – 40 8/ 96

= 3.55

29) $\widehat p$ = 32/119 = 0.2689

The test statistic is

p - p p(1-P)

  

0.2689 -0.36 0.36(1-0.36) 119

= -2.07

31) $\bar x$ = 43.4

s = 10.37

The test statistic is

α – s/ μ n

  

43.4 – 48 10.37/V10

= -1.403