Question

A student randomly selected 70 packets of sugar and weighed the contents of each packet, getting a mean of 3.586 g and a standard deviation of 0.074 g. Test the claim that the weights of the sugar packets have a mean equal to 3.5 g, as indicated on the label.

1.   Copy and paste the Minitab output for exercise into the document underneath the problem.   You are not also required to do these by hand, unless you want to.  

2. Write the rejection rule word for word as written here, "Reject Ho if the p-value is less than or equal to alpha."

3.   Write the actual p-value and alpha, then either "Reject Ho" or "Do not reject Ho." As an example: 0.0021 ≤ 0.05. True. Reject Ho.

4.    Write an English sentence stating the conclusion, claim, and significance level. As an example: If the claim is "Can we conclude that male business executives are taller, on the average, than the general male population at the  α  = 0.05 level?", and if we found our conclusion to be do not reject Ho, the sentence would be, "There is not enough evidence to conclude that  male business executives are taller, on the average, than the general male population at the  α  = 0.05 level."

Answer 1

as instructed in question i am uisng minitab to solve the problem.

here, as the sample sd (s) is given, i am using sample t tset for mean.

steps:-

stat basic statistics 1 sample t select summarized data from the drop down menu insample size type 70,in sample mean type 3.586,in standard deviattion type 0.074tick perform hypothesis test,in hypoothesized mean type 3.5 options in confidence leevl type 95,choose the laternative hypothesis as mean hypothesized meanokok.

**SOLUTION **

1).your minitab output be:-

One-Sample T

Descriptive Statistics

N	Mean	StDev	SE Mean	95% CI for μ
70	3.58600	0.07400	0.00884	(3.56836, 3.60364)

μ: mean of Sample

Test

Null hypothesis	H₀: μ = 3.5
Alternative hypothesis	H₁: μ ≠ 3.5

T-Value	P-Value
9.72	0.000

2.the rejection rule:-

reject the null hypothesis if,

p value   0.05 ()

( the p-value is less than or equal to alpha)

3. p value = 0.000

level of significance () = 0.05

decision:-

p value =0.000   0.05 () ...REJECT H0

4).conclusion:-

there is not sufficient evidence to support the claim that the weights of the sugar packets have a mean equal to 3.5 g at 0.05 level of significance.

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