A new engine has been developed. The developer claims that the engine will run for 4.5 hours (270 minutes) on a single gallon of regular gasoline. From the stock of 1500 engines a random sample of 50 enginges were selected for testing (average run of 265 minutes and standard deviation of 20 minutes). [br]Test the null hypothesis that the mean run time is 270 minutes against the alternative hypothesis that the mean run time is not 270 minutes. Use the significance level of 0.05. 

[table][tr][td][size=100]1.[br][/size][/td][td][size=100]Open the tab [i]Statistics[/i].[br][/size][/td][/tr][tr][td][size=100]2.[br][/size][/td][td][size=100]Choose the [i]T Test of a Mean[/i] as your preferred test from the drop-down list.[br][/size][/td][/tr][tr][td][size=100]3.[br][/size][/td][td][size=100]Enter the Null Hypothesis [math]\mu=270[/math].[br][/size][/td][/tr][tr][td][size=100]4. [/size][/td][td]Select the [i]Alternative Hypothesis[/i] option [math]\ne[/math].[/td][/tr][tr][td][size=100]5.[/size][/td][td]In the [i]Sample [/i]section, enter [math]Mean=165[/math],  standard deviation [math]s=20[/math], and sample size [math]N = 50[/math].[/td][/tr][tr][td][size=100]6.[/size][/td][td]Check the [i]Result[/i] section to interpret the relevant parameter values for your statistical test.[br][/td][/tr][tr][td][br][/td][td][b]Note:[/b] [i]GeoGebra [/i]automatically calculates the standard error of the mean ([i]SE[/i]), the t-score (t), and the corresponding probability based on a normal distribution ([i]P[/i]), and the degrees of freedom (df).[br][/td][/tr][/table]