An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 29 water samples and measure the pH of each. The sample mean and standard deviation are 6.7 and 0.35, respectively. Is there enough evidence to reject the company’s claim at the α = 0.05 level of significance?

No, there is not enough evidence to reject the company’s claim at the α = 0.05 level of significance.

Step-by-step explanation:

We are given that an industrial company claims that the mean pH level of the water in a nearby river is 6.8.

You randomly select 29 water samples and measure the pH of each. The sample mean and standard deviation are 6.7 and 0.35, respectively.

Let = mean pH level of the water in a nearby river.

SO, Null Hypothesis, : = 6.8   {means that the mean pH level of the water in a nearby river is 6.8}

Alternate Hypothesis, : 6.8   {means that the mean pH level of the water in a nearby river is different from 6.8}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

                        T.S.  =  ~

where,  = sample mean pH level = 6.7

             s = sample standard deviation = 0.35

             n = sample of water = 29

So, test statistics  =     ~

                               =  -1.539

Now at 0.05 significance level, the t table gives critical values of -2.048 and 2.048 at 28 degree of freedom for two-tailed test. Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean pH level of the water in a nearby river is 6.8 which means the company’s claim was correct.

tube or goog would be a great resource to with that question

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.