stRe Problem 4 A study indicates that keeping your icase yourgas mileage by at l

Question

stRe Problem 4 A study indicates that keeping your icase yourgas mileage by at least 2.4 mpg. To test this su es that keeping your automobile tires properly inflated durin ring the randomly sample 25 cars and find an average in winter months will increase your gas mileage by nd an average increase of 19 mpg with a standard dev this supposition, you ndard deviation of e Hypot .3 mpg when the tires are properly inflated. At the properly inflated. At the 0.045 level of significance, can nificance, can you refute 1 ve the claim of the study? alue(s) al Region Value

Explanation / Answer

Here, we have to use one sample t test for the population mean. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: Keeping automobile tires properly inflated during winter month’s increases gas mileage by 2.4 mpg on an average.

Alternative hypothesis: Ha: Keeping automobile tires properly inflated during winter month’s increases gas mileage by other than 2.4 mpg on an average.

H0: µ = 2.4 versus Ha: µ 2.4

This is a two tailed test.

We are given

Level of significance = alpha = 0.045

Sample size = n = 25

Degrees of freedom = n – 1 = 24

Sample mean = Xbar = 1.9

Sample standard deviation = S = 1.3

Critical values = 2.1150 and -2.1150

Critical region: |tcritical| > 2.1150

Test statistic formula is given as below:

Test statistic = t = (Xbar - µ) / [S/sqrt(n)]

Test statistic = t = (1.9 – 2.4) / [1.3/sqrt(25)]

Test value = t = -1.9231

P-value = 0.0664

Statistical decision

We do not reject the null hypothesis

Justification for Decision

Here, we are given the p-value = 0.0664 which is greater than the given level of significance or alpha value 0.045.

Discussion in contextual terms

We do not reject the null hypothesis, this means we conclude that there is sufficient evidence that keeping automobile tires properly inflated during winter month’s increases gas mileage by 2.4 mpg on an average.

Justification for Distribution Used:

For the given scenario, we do not given the population standard deviation and also sample size is small, so we use the t distribution. If we are given the population standard deviation and usually sample sizes are larger, then we use the Z or normal distribution.

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