Mathematics, 15.04.2020 05:18 officialgraciela67

A toy maker claims his best product has an average lifespan of exactly 18 years. A skeptical product evaluator asks for evidence (data) that might be used to evaluate this claim. The product evaluator was provided data collected from a random sample of 35 people who used the product. Using the data, an average product lifespan of 13 years and a standard deviation of 2 years was calculated. Select the 99%, confidence interval for the true mean lifespan of this product.

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Answer from: ciera51

99%, confidence interval for the true mean lifespan of this product is [12.08 years , 13.92 years].

Step-by-step explanation:

We are given that a toy maker claims his best product has an average lifespan of exactly 18 years.

The product evaluator was provided data collected from a random sample of 35 people who used the product. Using the data, an average product lifespan of 13 years and a standard deviation of 2 years was calculated.

Firstly, the pivotal quantity for 99% confidence interval for the true mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ t_n_-_1

where, $\bar X$ = sample average product lifespan = 13 years

n = sample of people = 35

s = sample standard deviation = 2 years

$\mu$ = true mean lifespan

Here for constructing 99% confidence interval we have used One-sample t statistics because we don't know about the population standard deviation.

So, 99% confidence interval for the true mean, $\mu$ is ;

P(-2.728 < t_3_4 < 2.728) = 0.99 {As the critical value of t at 34 degree

of freedom are -2.728 & 2.728 with P = 0.5%}

P(-2.728 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.728) = 0.99

P( $-2.728 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.728 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.728 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.728 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-2.728 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.728 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $13-2.728 \times {\frac{2}{\sqrt{35} } }$ , $13+2.728 \times {\frac{2}{\sqrt{35} } }$ ]

= [12.08 , 13.92]

Therefore, 99% confidence interval for the true mean lifespan of this product is [12.08 years , 13.92 years].

Answer from: Quest

step-by-step explanation:

this is not possible to solve with the info given. you need at least an one angle somewhere.

Answer fast and i’ll give you brainliest

Answer from: Quest

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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