Question

The data appearing in the data file was produced by randomly sampling n=48 2-litre bottles of a certain soft drink. As a quality control manager working for the company that bottles this soft drink, one of your responsibilities is to ensure that the 2-litre bottles are not be under-filled with product. It should be noted that the bottles can hold a maximum of 2.2 litres of product.

The data can be found in column 2 of the Download .csv file

1.98,1.99,1.98,1.97,1.97,1.98,1.98,1.98,1.98,1.99,1.97,1.99,1.98,1.99,1.97,1.98,1.98,1.98,1.97,1.99,1.97,1.98,1.99,1.98,1.97,1.97,1.98,1.99,1.98,1.97,1.97,1.99,1.98,1.99,1.99,1.98,1.98,1.99,1.98,1.99,1.98,1.99,1.98,1.99,1.99,1.98,1.98,1.98

(a) Does these data suggest that the bottles are being under-filled? Select the appropriate statistical hypotheses.

A. H0:μ≤2HA:μ>2H0:μ≤2HA:μ>2
B. H0:μ=2.2HA:μ≠2.2H0:μ=2.2HA:μ≠2.2
C. H0:μ=2HA:μ≠2H0:μ=2HA:μ≠2
D. H0:μ=2HA:μ<2H0:μ=2HA:μ<2
E. H0:μ<2HA:μ≥2H0:μ<2HA:μ≥2
F. H0:μ<2.2HA:μ≥2.2H0:μ<2.2HA:μ≥2.2
G. H0:X¯¯¯¯≥2HA:X¯¯¯¯<2H0:X¯≥2HA:X¯<2
H. H0:X¯¯¯¯<2HA:X¯¯¯¯≥2H0:X¯<2HA:X¯≥2
I. H0:μ≤2.2HA:μ>2.2H0:μ≤2.2HA:μ>2.2
J. H0:μ=2HA:μ≠2H0:μ=2HA:μ≠2

(b) Compute the value of the test statistic.

Test Statistic=

(use three decimals in your answer)

(c) Using the technology available to you compute the P-value.

P−value =

equation editor

(use five decimals in your answer)


(d) Testing at α=0.05 what decision can you make about the null hypothesis?

a) fail to reject b) rejct

(e) Complete the statement, providing your conclusion below.

From these data/This census/From this population of data , one can infer that the mean amount of soda dispensed into a 2-litre bottle is  ? less than/at most/ equal to/greater than ______ litres

(use one decimal in your answer).

Answer 1

A. H0:μ≤2HA:μ>2

critical value is -1.6 79

The t-value is -18.499

p value is 0.000001

critical value is greater than test statistic. so we have to reject null hypothesis.

mean is greater than 2

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