45 Use following information in Questions A hot dog manufacturer claims that one

Question

45 Use following information in Questions A hot dog manufacturer claims that one of his brands of hot dogs called So-Lean has an average fat content less than 1Sg per hot dog. Let l be the true mean fat content per hot dog in all the hotdogs of So-Lean brand. An independent testing organization is asked to analyze a random sample of 36 So-Lean hot dogs to assess if manufacturer's claim is correct Let R be an average fat content for this sample. Question#3 (8 points) Suppose that the sample resulted in a mean and standard deviation s-1g. dog mall the -18.6 Compute 95% confidence interval for -mean fat content per hot hotdogs of that brand. Use a proper procedure. Clearly show all work by hand. Question4 (8 points) Suppose 99% Confidence Interval for mean fat content per hot dog in all the hotdogs of that brand is (18.1 g, 19.1 g). Based on that interval, do you think that manufacturer's claim is correct? Clearly write a short explanation of your decision. Correct Not Correct circle one) Explanation:

Explanation / Answer

Solution3:

Null hypothesis is

Ho:=18

Alterbative Hypothesis is

H1 <18

H1 is claim

alpha=0.05

95% confidence interval for mean is

sample mean-tcrit*sample sd/sqrt(n),sample mean+tcrit*sample sd/sqrt(n)

Degrees of freedom=n-1=36-1=35

alpha=0.05

alpha/2=0.05/2=0.025

t crit=1.689

sample mean-tcrit*sample sd/sqrt(n),sample mean+tcrit*sample sd/sqrt(n)

18.6-1.689 (1/sqrt(36),18.6+1.689 (1/sqrt(36)

18.3,18.9

lower limit=18.3

upper limit=18.9

18.3<<18.9

since claim value 18 is not in the interval range.

Reject Null hypothesis

Accept Alternative Hypothesis

Conclusion:

there is sufficent statistical evidence at 5% level of significance to support the cliam that average fat content less than 18.

Solution4:

99% confidence intervalfor mean is 18.1 to 19.1

lower limit=18.1

upper limit=19.1

18.1<<19.1

Hypothesised value of 18 is not in the confidence interval range.

Reject Null hypothesis

Accept alternative Hypothesis

there is sufficent statistical evidence at 1% level of significance to support the cliam that average fat content less than 18.

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