A sample of 14 cans of DZUSI DZUS soda gave a mean number of 23 calories per can

Question

A sample of 14 cans of DZUSI DZUS soda gave a mean number of 23 calories per can with a variance of 9 calories?. Another sample of 16 cans of CHI BAR TSODA gave a mean number of calories of 25 per can with a variance of 16 calories?. At a 1% significance level, can you conclude that the mean number of calories per can of soda is different for these two soft drinks? Find: a. The point estimate for the population means. b. The "H_0" and "H_a" statements c. The test statistic. d. What is your conclusion? Explain. Chris, of Bhak Dat Stat Up! (a Tsygylyk subsidiaryl, wanted to test the claim that the standard deviation for the number of months in a relationship, before a couple had their first argument, would be at least 5 months. He randomly surveyed forty couples and found their mean to be 12.9 months with a standard deviation of 3.1 months. At a 5% significance level, can he conclude that the standard deviation for all such couples is at least 5 months? The SolJah Boiz, Luis, Jackson and Riccardo, wanted to estimate the difference between the percentages of users of toothpastes who will never switch toothpaste. They took a sample of 500 users of Decay Toothpaste (100 of who said that they would never switch) and 400 users of Cavity Jamm (68 of who said that they would not switch). a. Let p_1 - p_2 represent the two groups that use the above products. b. Construct a 97% confidence interval for the difference between the proportions of all users of the two toothpastes who will never switch.

Explanation / Answer

SOLUTION4A:

point estimate is sample mean

point estimates for DZUSI DZUS IS 23 and point estimate for CHI-BAR T SODA=25

Solution4b:

Null hypothesis:

H0:(DZUSI )= CHI-BAR T SODA

ALternative hypothesis

H1:(DZUSI ) CHI-BAR T SODA

alpha=1%=0.01

t=(23-25)-0/sqrt[9/14+16/16]

t =-1.56

Solutiond:

df=n1+n2-2=14+16-2=28

P = 0.129

p>0.01

Fail to reject Null hypothesis.

conclusion:there is no sufficient evidence at 1% level of significance to conclude that means are different.

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