A research paper reports, "… in a sample with 350 observations, the sample average Y = 0.9 is statistically significantly different from zero at a 5% level, since its t‐statistic is 3.0." Suppose you want to test the null hypothesis that the true mean of the population is equal to one, not zero. Would you reject this null hypothesis (against a two‐sided alternative) at a 5% level?

I would reject the null hypothesis.

Step-by-step explanation:

The test is a two-tailed test because it is stated that the alternate hypothesis is two-sided.

Degree of freedom = n - 1 = 350 - 1 = 349

At 349 degrees of freedom and 5% significance level, the critical values are -1.96702 and 1.96702

Conclusion:

Reject the null hypothesis because the test statistic 3 falls outside the region bounded by the critical values -1.96702 and 1.96702.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.