Problem #2
Bumble likes going to his local Subway and always orders a foot-long meatball sandwich there, as he finds the satisfaction he gets from a foot-long sandwich to be priceless. Over the past month, however, Bumble has been constantly hungry. He suspects the meatball sandwiches at his local Subway to be shrinking on average. Bumble has randomly sampled 20 of those ‘supposedly’ one-foot-long (12 inches) meatball sandwiches at that local Subway and has found a sample mean length of 11.8 inches with a sample standard deviation of 0.30 but does not know what to conclude from there. Please answer the following questions to help Bumble conduct an appropriate test to see if the mean length is shrinking at the 0.01 level of significance.
2-1 State the appropriate H_{0} and H_{1} for this test.
Separately fill in the parameter, equality, and value by reporting letters respectively from the following list to complete each hypothesis.
H_{0}: - select -abcdef - select -abcdef - select -abcdef
H_{1}: - select -abcdef - select -abcdef - select -abcdef
parameter equality value
2-2 What would be the most appropriate critical value (i.e., z_{crit} or t_{crit}) for this test?
Separately fill in the name, sign, and value by reporting letters respectively from the following list to complete the critical value (e.g., to together state z_{crit} = +1.96).
- select -abcdef = - select -abcdef - select -abcdef
name: sign: value:
c. ± c. 2.539
d. 2.528
e. 1.96
f. 1.645
2-3 What is the p-value for this test?
Select from the list below and report the letter. - select -abcdef
2-4 Bumble thinks the p-value is the probability that the sandwiches are shrinking in size. Is this true? Please correct him if needed and interpret the p-value by directly explaining what this probability itself means.
Select the most appropriate statement from the list below and report the letter. - select -abcdef
2-5 What is the most appropriate conclusion for this hypothesis test?
Select the most appropriate statement from the list below and report the letter. - select -abcdef
2-1:
2-2
2-3:
From t table, for df =19 and t = -2.981 the p-values is less than less than 0.005.
2-4
Correct option :
No, Bumble is wrong. The p-value indicates the probability of a sample mean being 11.8 inches or less if the true average length is really 12 inches.
2-5:
Correct option:
Reject H0 and conclude that the sandwiches are smaller than 12 inches on average.
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