10. (0.5 +1+1 + 1 + 0.5 = 4 marks) To compare the mean weights of cans with corn produced by the company | and by the company Il, random sample of size #7; = 10 was selected from population of cans produced by company |, and random sample of size 77, = 16 was selected from population of cans produced by company Il The weights of the cans in each of two samples were measured, and sample means and sample standard deviations were calculated. Calculated values of sample means and sample standard deviations are given in the following table: X,=658 X,=652g =8 For both companies the weights of the cans are normally distributed random variables. Do the data provide sufficient sample evidence to indicate a difference in mean weights of cans produced by the company | and company II? Test appropriate hypotheses. Use & = 0.01 . Assume that population variances for both population of weights may be assumed equal and common population variance is estimated with the value of pooled sample variance. a. State null and research hypotheses about the difference in the mean weights of cans produced by company | and company Il H: H, . b. Calculate the value of pooled sample variance. Keep three digits after decimal point in the answer. Show your work in finding pooled sample variance. The value of pooled sample variance is 5. c. State the observed value of test statistic. Keep three digits after decimal point in the answer. Show your work in finding the observed value of test statistic. The observed value of test statistic is "nh.e = d. State the rejection region (in the form of inequality). The rejection region is e. Decide whether null hypothesis is rejected or is not rejected, and insert the word rejected or the words not rejected into the following statement. Null hypothesis is atex =0.01 . Insert the word sufficient or insufficient into the following statement. There is sample evidence to conclude that there is a difference in mean weights of cans with corn produced by the company | and company Il