6. (from Q32 P. 594) Some students checked 6 bags of Doritos marked with a net w

Question

6. (from Q32 P. 594) Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5 a. (1 mark) Calculate the sample incall, aud its standard error s/vn. b. (2 marks) Create a 95% confidence interval for the mean weight of such bags. c. (3 marks) State Ho and Ha and calculate a p-value if we want to show that the true mean weight of all such bags is actually greater than 28.3 grams. d. (3 marks) State your conclusion, referring to both the confidence interval and the p-value.

Explanation / Answer

a) mean = 28.9833
standard error = std.dev./sqrt(n)
= 0.3601/sqrt(6) = 0.1470

b) t value at 95% = 2.5706

CI = mean + /- t * SE
= 28.9833 +/- 2.5706 * 0.1470
= (28.6054,29.3612)

c)
H0 : mu = 28.3
Ha : mu > 28.3

Test statistics:

t = ( x - mean) / ( s/sqrt(n))
= ( 28.9833 - 28.3) / (0.3601/sqrt(6))
= 4.6480

P value = .0028

d)
By confidence interval it does not contain null hypothesis so,we reject the null hypothesis

By p value we reject the null hypothesis because p value is less than 0.05 significance level

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