Question

A nationwide study a few years ago showed that American women, ages 19-30, consume an average of 110 milligrams of caffeine per day. Recently a group of Stats students decided to test whether the average was more than that now. They obtained a random sample of 25 American women, ages 19-30, whose average daily consumption was 115 milligrams of caffeine per day. The standard deviation was s = 14, and a histogram was unimodal and nearly symmetric with no outliers. Perform a hypothesis test using 0.05 as the significance level. Check conditions after writing your hypotheses, show all calculations, and interpret your results in context at the end.

Answer 1

Answer:

Here claim is that mean is greater than 110

So hypothesis is vs

As n<30 and population standard deviation not know so we will use t statistics

Further distribution is symmetric with no outliers, so we get that distribution is normal

P value is TDIST(1.79,24,1)=0.043<alpja=0.05, so we reject the null hypothesis

Hence there is sufficient evidence to support the claim that mean is greater than 110

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