Question

Based on a random sample of 25 units of product x, the average weight is 102 lb and the sample standard deviation is 10 lb. we would like to decide if there is enough evidence to establish that the average weight for the population of product x is greater than 100 lb. therefore, the alternative hypothesis can be written as ha: μ > 100. (assume the population is normally distributed.)

Answer 1

Answer:

No, we don't have enough evidence to establish that the average weight for the population of product x is greater than 100 lb.

Step-by-step explanation:

We are given the sample average weight, xbar = 102 lb

                       and sample standard deviation, s = 10 lb

We have test that is there enough evidence to establish that the average weight for the population of product x is greater than 100 lb.

So, Null Hypothesis, $H_0$ : $\mu$ = 100 lb (Population mean weight is equal to 100

                                                                     lb)

Alternate Hypothesis, $H_1$ : $\mu$ > 100 lb (Population mean weight is greater

                                                                 than 100 lb)

Since, population is normally distributed so;

   Test Statistics = $\frac{x - \mu}{\frac{s}{\sqrt{n} } }$ follows $t_n_-_1$

                            = $\frac{102 - 100}{\frac{10}{\sqrt{25} } }$ follows $t_2_4$  = 1

So, we assume that level of significance is 5% so at this level t table gives critical value of 1.711 at 24 degree of freedom. Since our test statistics is less than the critical value so we have insufficient evidence to reject null hypothesis as our test statistics does not fall in the rejection region as 1.711 > 1.

Therefore, we don't have enough evidence to establish that the average weight for the population of product x is greater than 100 lb and conclude that average weight for the population of product x is 100 lb.