i need help anyone?

Question

According to a 2020 study, the average cost of gas, oil, tires, and maintenance on commuters who travel 15,000 miles per year in their own vehicles was $1770. A recent study based on 300 such commuters found that the mean of such expenses is $1840 per year with a standard deviation of $460. Find the p – value for the test with the alternative hypothesis that the current mean of such costs is different from $1770. Would you reject the null hypothesis at α = 0.01?                                                     

Answer 1

Ho: mu = 1770

Ha: mu != 1770

since sample size is large (300), we can use standard normal distribution (z)

z = (mean - mu)/(SD/sqrt(sample size)) = (1840 - 1770)/(460/sqrt(300)) = 2,64

p-value = P(z > 2.64) + P(z < -2.64).

P(z < -2.64) = 0.0041

since normal distribution is symmetric

P(z > 2.65) = 0.0041

p-value = 0.0041 + 0.0041 = 0.00823

since p-value is less than alpha = 0.01, the null hypothesis would be rejected