Question

1. 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

Given that, sample size (n) = 29, sample mean = 31.1 minutes and sample standard deviation (s) = 3.7 minutes

The null and alternative hypotheses are,

H0 : μ = 30 minutes

Ha : μ ≠ 30 minutes

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = t = 1.601

Degrees of freedom = 29 - 1 = 28

Using Excel we find the p-value as follows :

Excel Command : =TDIST (1.601, 28, 2) = 0.1206

=> p-value = 0.1206

Since, p-value is greater than 0.01 significance level, we fail to reject the null hypothesis (H0).

Conclusion : There is not sufficient evidence to warrant rejection of the claim that the true mean time is 30 minutes.