A botanist claims that the mean concentration of glucose in a plant\'s stem is a

Question

A botanist claims that the mean concentration of glucose in a plant's stem is about 0.3 M. As a result, a young researcher determines the concentration of 12 plants and obtains the following results: 0.2, 0.5, 0.25, 0.43, 0.25, 0.25, 0.38, 0.15, 0.2, 0.3, 0.5, 0.31 With a 10% significance level, the young researcher wants to determine that the mean concentration is different than 0.3. (a) Identify the null and alternative hypothesis. (b) Find the test statistic. (c) What can you conclude based on your hypothesis. Prove this using critical values.

Explanation / Answer

(A) Below are the null and alternate hypothesis

H0: mu = 0.3

Ha: mu not equals to 0.3

(B) From the given sample data we have

Test statistics, t = (0.31 - 0.3)/(0.1126/sqrt(12)) = 0.3077

(C) For 90% significance level, critical value of test statistics = 1.7959. As test statistics is less than critical value, we fail to reject the null hypothesis. This means there are not sufficient evidence to conclude that mean concentration of glucose in plant stem is not equals to 0.3

mean 0.31 std. dev. 0.1126 n 12

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