Question

Exercise 3 Iron Man is checking out a new suit that fires lasers more accurately. If he is aiming for a bullseye, his original suit fires lasers that deviate from their target with a standard deviation of 2mm. Ironman collects 16 measurements from his new suit and finds that it fires lasers with a sample standard deviation of s = 1.6mm. Parts (a) - (b), state the following, showing work where appropriate: null and alternative hypothesis distribution and value of the test statistic p value conclusion (reject or fail to reject ). a. (1 point) Perform a hypothesis test at to test whether there is sufficient evidence to suggest that the new suit is better (more accurate) than the original. b. (1 point) Suppose that Ironman takes 100 measurements and still finds a sample standard deviation of 1.6mm. Perform a hypothesis test at to test whether there is sufficient evidence to suggest that the new suit is better (more accurate) than the original. c. (0.5 points) (2 parts) Perform the hypothesis test in part (b) using

Answer 1

Answer: (a). insufficient evidence.

(b). sufficient evidence

(c). insufficient evidence

Explanation:

we will analyse this carefully to help us understand it better.

we have the standard deviation for the original suit = 2mm

standard deviation for new suit = 1.6mm

given n = 1.6

from the question we know that the suit with less standard deviation is better than the other suit

considering a null hypothesis;

H₀ : б ≥ 2, (here the new suit is not better than the original alternative hypothesis).

Also Hi : б < 2 (we have here that the new suit is better than the original )

using the Chi-Square distribution with n-1 degree of freedom to test the claim about the value of the standard deviation;

X² = (n-1) s²/ б² = (16-1)(1.6)² / (2)² = 9.6

taking the P value of X² (9.6) for 15 D O F from the P value table gives us

1-0.8441 = 0.1559

also ∝ = 0.05

where P-value > ∝ (0.05)

we can see from here that there is insufficient evidence to claim that new suit is better than that of the original suit, having failed to neglect H₀

(b). Given n = 100 and s = 1.6

then we have that X² = (n-1) s²/ б² = (100-1)(1.6)² / (2)² = 63.36

P-value of X² at 99 dif gives 0.0020

where ∝ = 0.05

since P value < ∝

rejecting the null hypothesis H₀,

we can safely say that there is sufficient claim that the new suit is better than the original at 95%.

(c). where we have that ∝ = 0.001

for part(b) P-values = 0.0020

given P-value > ∝ ;

we fail to neglect the null hypothesis.

From this we can say that the is insufficient evidence backing the claim thhat the new suit is better than the original suit at 99.99% confidence level.

cheers i hope this helps!!!!!