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a doctor claims that people are more than 11 pounds overweight. to test the claim, 25 randomly selected people were weighed and the difference between their actual weight and their ideal weight was calculated. the sample mean and sample standard deviation of that difference were12 and 4 pounds, respectively. assuming a paired t-test is appropriate, can we conclude at the 1% level of significance that the claim is true? group of answer choices yes, conclude the claim is true by accepting h0.

Answer :

There is enough evidence to conclude that the doctor's claim is true.

We have given that,

population mean μ = 11 pounds

sample size n = 25

sample mean x = 12 ponds

standard deviation σ = 4 pounds

so the null hypothesis is H₀ : μ = 11 pounds

and the alternative hypothesis is Hₐ : μ > 11 pounds

now we will calculate test statistics,

t = (x-μ)/(σ/√n)

 = (12 - 11)/(4/√25)

 = 1/(4/5)

t = 1.25

p-value from the z-table is 0.10565

the result is non significant at p < 0.01.

Hence the null hypothesis rejected .

Therefore there is enough evidence to conclude that the doctor's claim is true.

The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.

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