Bastien, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per gallon. You conduct a test with a 0.05 level of significance to determine whether or not the manufacturer's advertising campaign is legitimate. What is the p-value associated with the sample results (2 decimals)?

We conclude that the the manufacturer's advertising campaign is not correct.

P-value of test = 0.067.

Step-by-step explanation:

We are given that an independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per gallon.

We have to conduct a test to determine whether or not the manufacturer's advertising campaign is legitimate.

Let = population average gasoline of new small cars in highway driving.

SO, Null Hypothesis, : 50 miles per gallon   {means that the manufacturer's advertising campaign is not correct}

Alternate Hypothesis, : > 50 miles per gallon   {means that the manufacturer's advertising campaign is correct}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

                         T.S.  =  ~ N(0,1)

where,   = sample average gasoline = 51.5 miles per gallon

              = population standard deviation = 6 miles per gallon

              n = sample of automobiles = 36

So, test statistics  =   

                               =  1.50

Now at 0.05 significance level, the z table gives critical value of 1.6449 for right-tailed test. Since our test statistics is less than the critical values of z as 1.50 < 1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Also, P-value is given by the following formula;

         P-value = P(Z > 1.50) = 1 - P(Z 1.50)

                                            = 1 - 0.93319 = 0.067 or 6.7%

Therefore, we conclude that the the manufacturer's advertising campaign is not correct as its new small cars average less than or equal to 50 miles per gallon in highway driving.

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answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.