Question

A toy maker claims his best product has an average lifespan of exactly 14 years. A skeptical quality control specialist asks for evidence (data) that might be used to evaluate this claim. The quality control specialist was provided data collected from a random sample of 45 people who used the product. Using the data, an average product lifespan of 19 years and a standard deviation of 4 years was calculated. Select the 99%, confidence interval for the true mean lifespan of this product.

Answer 1

Answer:

interval = [17.3948 , 20.6052]

Step-by-step explanation:

given,

random sample (n) = 45

average product lifespan = 19 years

standard deviation = 4 years

confidence interval of 99 %  = ?

we know,

t* = qt(1.99/2 + 44 ) = qt(0.995,44)

t* = 2.692

so,

interval

$x = 19 \pm t* \times (\dfrac{s}{\sqrt{n}})$

$x = 19 \pm 2.692 \times (\dfrac{4}{\sqrt{45}})$

$x = 19 \pm 2.692 \times 0.5963$

$x = 19 \pm 1.6052$

interval = [19 - 1.6052 , 19 + 1.6052]

interval = [17.3948 , 20.6052]