Question

(1 point) In a sample of 40 grown-ups, the mean assembly time for a boxed swing set was 1.86 hours with a standard deviation of 0.46602 hours. The makers of this swing set claim the average assembly time is less than 2 hours.

(a) Find the test statistic.

(b) Test their claim at the 0.01 significance level.

Critical value:

Is there sufficient data to support their claim?
Yes
No

(c) Test their claim at the 0.05 significance level.

Critical value:

Is there sufficient data to support their claim?
Yes
No

(1 point) Ben thinks that people living in a rural environment have a healthier lifestyle than other people. He believes the average lifespan in the USA is 77 years. A random sample of 20 obituaries from newspapers from rural towns in Idaho give ?¯=78.81 and ?=1.86

. Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years?

(a) State the null and alternative hypotheses: (Type "mu" for the symbol ?

, e.g. mu >1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)
?0 :
??

:

(b) Find the test statistic, t =

(c) Answer the question: Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? (Use a 10% level of significance)
(Type: Yes or No)

(1 point) The hypothesis test

?0:?=36?1:?≠36

is to be carried out. A random sample is selected, and yields ?¯=38 and s = 15. If the value of the t statistic is ?=0.692820323027551

, what is the sample size? (If rounding is required, round to the nearest integer.)

Sample Size =

Answer 1

To test the claim that the makers of this swing set claim the average assembly time is less than 2 hours, we use one sample t test because population standard deviation unknown.

H₀ :µ = 2 hour
H₁ :µ < 2 hours

From the given information,

Sample size = 40, sample mean = 1.86 hours, Sample standard deviation = 0.46602 hours

Here we conduct one sample t test

1. Test statistics

T = (1.86 - 2) / (0.46602/sqrt(40))

Test statistics (t) = -1.90

2. T critical value for one tailed test with 0.01 level of significance and degrees of freedom = n-1 = 39

            T_c = T_{0.01, 39} =T.INV(0.01,39) = -2.426

Test statistics T = -1.90 > T_c = -2.426 so we failed reject H₀.
No, there is not sufficient data to support the claim that the average assembly time is less than 2 hours at 0.05 level of significance.

3. T critical value for one tailed test with 0.05 level of significance and degrees of freedom = n-1 = 39

      T_c = T_{0.01, 39} =T.INV(0.05,39) = -1.685

     Test statistics T = -1.90 < T_c = -1.685 so we reject H₀.

Yes, there is sufficient data to support the claim that the average assembly time is less than 2 hours at 0.05 level of significance.

To test the claim that that people living in rural Idaho communities live longer than 77 years, we use one sample t test because population standard deviation unknown.

1. H₀ :µ = 77 years

   H_a :µ > 77 years

From the given information,

Sample size = 20, sample mean = 78.81, Sample standard deviation = 1.86

Here we conduct one sample t test

2. Test statistics

T = (78.81 - 77) / (1.86/sqrt(20))

Test statistics (t) = 4.3519

3. T critical value for one tailed test with 0.10 level of significance and degrees of freedom = n-1 = 19

T_c = T_{0.10, 19} =T.INV(0.10,19) = 1.328

Test statistics T = 4.3519 > T_c = 1.328 so we reject H₀ at 10% level of significance.

Yes, this sample provides evidence that people living in the rural Idaho communities live longer than 77 years at 0.10 level of significance.

H₀ :µ = 36

H_a :µ ≠ 36

From the given information, Test statistics (t) = 0.692820323027551

Sample size = n, sample mean = 38, Sample standard deviation (s)= 15

Here we conduct one sample t test

Test statistics (t) = (38 - 36) / (15/sqrt(n))

0.692820323027551 = (38 - 36) / (15/sqrt(n))

n = (0.692820323027551*15/2)²

n = 27

Sample size = 27