6. A research article reported that for a random sample of 850 meal purchases made at fast food chain A, the mean number of calories was 1,001, and the standard deviation was 481. For a random sample of 2,108 meal purchases made at fast food chain B, the mean number of calories was 905, and the standard deviation was 626. Based on these samples, is there convincing evidence that the mean number of calories in fast food chain B meal purchases is less than the mean number of calories in fast food chain A meal purchases?

MATLAB: An Introduction with Applications
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6. A research article reported that for a random sample of 850 meal purchases made at fast food chain A, the mean number of calories was 1,001, and the standard deviation was 481. For a random sample of 2,108 meal purchases made at fast food chain B, the mean number of calories was 905, and the standard deviation was 626. Based on these samples, is there convincing evidence that the mean number of calories in fast food chain B meal purchases is less than the mean number of calories in fast food chain A meal purchases? (Test the relevant hypotheses using a 0.05 level of significance. Use ?1 for fast food chain B and ?2 for fast food chain A.)

State the appropriate null and alternative hypotheses.
H0: ?1 − ?2 > 0
Ha: ?1 − ?2 < 0
 
H0: ?1 − ?2 = 0
Ha: ?1 − ?2 < 0
    
H0: ?1 − ?2 < 0
Ha: ?1 − ?2 > 0
 
H0: ?1 − ?2 < 0
Ha: ?1 − ?2 = 0
 
H0: ?1 − ?2 = 0
Ha: ?1 − ?2 > 0
 
t=_______
P-value=_____
 
State the conclusion in the problem context.
 
A) We fail to reject H0. There is convincing evidence that the mean number of calories in fast food chain B meal purchases is less than the mean number of calories in fast food chain A meal purchases.
 
B) We fail to reject H0. There is not convincing evidence that the mean number of calories in fast food chain B meal purchases is less than the mean number of calories in fast food chain A meal purchases.    
 
C) We reject H0. There is not convincing evidence that the mean number of calories in fast food chain B meal purchases is less than the mean number of calories in fast food chain A meal purchases.
 
D) We reject H0. There is not convincing evidence that the mean number of calories in fast food chain B meal purchases is less than the mean number of calories in fast food chain A meal purchases.
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