Question

Find the null and alternative hypothesis of the following:

1. 25 brand A cigarettes had an average nicotine content of 5mg, while 40 brand B cigarettes had an average nicotine content of 4.8mg. If the standard deviation of nicotine content if 1.6mg, does brand B have a lesser nicotine content with a 96% confidence level?
2. Fifteen pupils from an international school have a mean of 110 and a variance of 64 while 20 pupils from an integrated school have a mean IQ of 114 and a variance of 78. Is there a significant difference between their mean IQs using a 0.02 level of significance?

Answer 1

1.

Let $\mu_A$ denote an average nicotine content for brand A and $\mu_B$ denote an average nicotine content for brand B, hence:

$H_0: \mu_A-\mu_B=0$

$H_a:\mu_A-\mu_B>0$

2.

Let $\mu_1$ denote a mean IQ for pupils from an international school and $\mu_2$ denote a mean IQ for pupils from an integrated school, hencde:

$H_0:\mu_1=\mu_2$

$H_a:\mu_1\ne\mu_2$