Question

A machine in the lodge at a ski resort dispenses a hot chocolate drink. The average cup of hot chocolate is supposed to contain u = 8 ounces. We may assume that x follows a normal distribution with standard deviation r = 0.3 ounces. A random sample of 16 cups of hot chocolate from this machine had a mean content of x bar = 7.5 ounces. Use a a = 0.05 level of significance and test whether the mean amount of liquid is less than 7.5 ounces.

Answer 1

Note that we always test the claim is correct or not. Here claim was that population average cup of hot chocolate is supposed to contain 8 ounces. Consider that population average is considered as $\mu$ ​​​​​​.

The 7.5 is the sample mean, in hypothesis testing we never test sample mean, we always test claim of population.

We hawe to teat: Ho Mean amount ounees CN t Mean amount iid 8 u SUnces Ho: M-8 441A 0 yiren Sumpls n 169 7-5 oune meorn -ample size e Populatien stondand deviation 3 ouneus'NS s tatistie!- Teat Ho N CO1) o8hyte puhth meau) Heres 7.5-8 ニー6.666子 .3 N16

ivan en dzo.05 The teat n tai hed We at 7ivan aampl O05 for obsd -T5= 4.6 45 Z O.05 Herej 6.666t obsel z 1.64 5 tHo Hence Serk sW net fae mean Comeludi fhat We can lere than amount ounees

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