Summary statistics are given for independent simple random samples from two populations. Use the nonpooled t-test to conduct the required hypothesis test. 1 = 75.1, s 1 = 4.5, n 1 = 11, 2 = 66.2, s 2 = 5.1, n 2 = 9 Perform a two-tailed hypothesis test using a significance level of α = 0.01.

The decision rule is  

Reject the null hypothesis

Step-by-step explanation:

From the question we are told that

   The first sample mean is  

    The first sample standard deviation is  

    The first sample size

    The second sample mean is  

    The second sample standard deviation is  

     The second sample size is  

     The significance level is  

The null hypothesis is  

The alternative hypothesis is  

Generally the pooled standard deviation is mathematically represented as

=>  

=>  

Generally the degree of freedom for the is mathematically represented as

=>  

=>  

Generally the test statistics is mathematically represented as

=>

=>

Generally the student distribution table the probability of   to the right at a degree of freedom of    is  

Generally the p-value is mathematically represented as

=>    

=>    

From the value obtained we see that   hence we

The decision rule is  

Reject the null hypothesis

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,