Question

9.    The time in minutes taken by a biological cell to divide into two cells has a

           normal distribution. When a sample of twenty-nine cells were observed, the mean

           time taken by them to divide into two was 31.1 minutes with a standard deviation

           of 3.7 minutes. At α = .01, test the claim that the true mean time is 30 minutes.

Answer 1

Here n<30 so we will use a t distribution..

Here claim is true mean is 30.So the null and alternate hypothesis are:

$H_0:\mu=30$

$H_a:\mu\neq30$

As the alternate hypothesis has an not equal sign it is a two tailed test.

Now we will find test statistic.

$t=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{31.1-30}{\frac{3.7}{\sqrt{29}}}=1.600$

degree of freedom =n-1=29-1=28

Now P-value for two tailed test at alpha=0.01 and d.f 28 =TDIST(1.60,28,2)=0.121

As P-value(0.121) is greater than alpha we fail to reject the null hypothesis.

So we have sufficient evidence to support the claim that true mean time is 30 minutes.