Question

in a sample of 50 cars, it was found that the mean gas consumed per week is 12 gallons. population statistic shows that mean gas consumed per week is 9.5gallons with a standard deviation of 5 gallons. At 0.01 level of significance, test the claim that the mean gas consumed per week is more than 9.5gallons.

Critical Value:

Test Statistics:

Conclusion Regarding the null hypothesis:

your statement regarding the claim:

Answer 1

Here we reject null hypothesis.

X be the per week . to random variable denoted gas consumed consumed per week X be the sample mean of gas Therefore, X = 12 gallons be the sample size, n=50 N be the population mean, N=9.5 gallons and I be the standard deviation, so 5 gallons . the Now, the Hypotheses Ho : N=9.5 VS . Hi : Ny 9.5 The Critical value at 0.01 30.01 - 2.33 level of significance is [We get the critical value at 0.01 level of significance from Critical Value Table Test statistic, Now, z u r Here x ~ Normal (N=9.5,8=5 ) Therefore Normal (N=9.5 ,8/sn = 5 / 50 ) Now, Test statistic x-N z = 11 When 12-9.5 - 3.53 5 1/50 z value is greater than critical value z* we reject the null hypothesis otherwise we accept the null hypothesis. Hote 7 = 3.53 Y Z4.04 = 2.33 therefore we reject the nell hypothesis.