61 sample problems. The new algorithm completes the sample problems with a mean time of 14.06 hours. The current algorithm completes the sample problems with a mean time of 16.43 hours. Assume the population standard deviation for the new algorithm is 3.004 hours, while the current algorithm has a population standard deviation of 4.568 hours. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Le

There is sufficient evidence to conclude that the new algorithm has a lower mean completion time than the current algorithm

Step-by-step explanation:

From the question we are told that

    The  sample size for each algorithm is

     The sample mean  for new algorithm is  

     The  standard deviation for new algorithm is  

     The  sample  mean for  the current algorithm is  

     The standard deviation for current algorithm is  

     The  level of significance is

The  null hypothesis is  

The  alternative  hypothesis is

Here   are population mean for  new and current algorithm

Generally the test statistics is mathematically represented as

=>    

=>    

Generally the p-value is mathematically represented as

From the  z-table  

=>    

From the calculated value  we see that    hence the null hypothesis is rejected

        Hence we can conclude that there is sufficient evidence to conclude that the new algorithm has a lower mean completion time than the current algorithm

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.