Question

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4. National Fue!saver Corporation manufactures the Platinum Gasaver, a device they claim “may increase gas mileage by 30%." Here are the percent changes in gas mileage for 15 identical, randomly-selected vehicles, as presented in one of the company's advertisements 2.4 6.9 10.410.8 24.8 28.7 28.733.734.6 38.5 40.244.646.846.948.3 (a) The sample mean is x = 29.43 and the sample standard deviation is s = 16.23. Calculate and interpret the standard error of the mean for these data. (b) Construct and interpret a 90% confidence interval to estimate the mean change (in percent) in gas mileage. Does the data support the company's claim? Use the four-step process

Answer 1

Question

(a) Here the sample mean = $\bar x$ = 29.43

sample standard deviation = s = 16.23

sample size =n = 15

standard error = s/sqrt(n) = 16.23/sqrt(15) = 4.19

Here standard error of sample mean means that it is the actual or estimated standard deviation of the error of the sample means distribution In other words, it is the actual or estimated standard deviation of the sampling distribution of the sample statistic, in this case sample mean of percent change.

(b) Here

Step 1 : Defining sample mean and standard error of the mean

sample mean =  $\bar x$ = 29.43

standard error = se₀ = 4.19

Step 2 : Confidnece interval = 90%

Step 3 :

Calculating margin of error

Margin of error = critical test statistics * standard error of sample mean

Degree of freedom = dF = 15 - 1 = 14

t_critical for dF = 14 and alpha = 0.10

t_critical = 1.7613

Margin of error = 1.7613 * 4.19 = 7.381

Step 4 :

90% confidence interval = sample mean +- margin of error

= 29.43 +- 7.38

= (22.05, 36.81)

so here as the value of 30% as claimed by the company is in the the confidence interval so data support the compay's claim.