Question

The means of the number of revolutions per minute of two competing engines are to be compared. Thirty engines are randomly assigned to be tested. Both populations have normal distributions. Table given below shows the result. Do the data indicate that Engine 2 has higher RPM than Engine 1? Test at a $5\%$level of significance.

Engine	Sample mean number of RPM	Population Standard Deviation
1	1500	50
2	1600	60

Short answer

There is sufficient evidence to conclude that the Engine $2$runs at a higher RPM than Engine $1.$

Step-by-step solution

Given information

The given table shows two samples:

Engine	Sample Mean Number Of RPM	Population Sample standard deviation
1	1500	50
2	1600	60

The mean of the number of revolutions per minute of two competing engines is to be compared. Thirty engines are randomly assigned to be tested. Both populations have a normal distribution. Test at a $5\%$level of significance.

Calculation

The null hypothesis is

$$\begin{gathered} H_0:{\mu }_1\le {\mu }_2 \\ {H}_a:{\mu }_1<{\mu }_2 \end{gathered}$$

The significant level, $\alpha =5\%=0.05.$.

The p-value is almost zero, so we reject the null hypothesis.

Hence, there is sufficient evidence to conclude that Engine $2$runs at a higher RPM than Engine$1.$