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.

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. =  ~

where, = sample average product lifespan = 13 years

            n = sample of people = 35

            s = sample standard deviation = 2 years

            = 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, is ;

P(-2.728 < < 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 < < 2.728) = 0.99

P( < < ) = 0.99

P( < < ) = 0.99

99% confidence interval for = [ , ]

                                         = [ , ]

                                         = [12.08 , 13.92]

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

11

step-by-step explanation:

32.50-7.50=25

225/25=11

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