A machine in the lodge at a ski resort dispenses a hot chocolate drink. The average cup of hot chocolate is supposed to contain µ = 7.75 ounces. A random sample of 16 cups of hot chocolate from the machine had a mean content x = 7.62 ounces with standard deviation s = 0.3 ounces. Use 0.05 level of significance and test whether the mean amount of liquid is less than 7.75 ounces.
Sample size = n = 16
Sample mean = = 7.62
Standard deviation = s = 0.3
Claim: The mean amount of liquid is less than 7.75 ounces.
The null and alternative hypothesis is
Level of significance = 0.05
Here population standard deviation is unknown so we have to use
t-test statistic.
Test statistic is
Degrees of freedom = n - 1 = 16 - 1 = 15
Critical value = 1.753 ( Using t table)
Test statistic < critical vaue we fail to reject null hypothesis.
Conclusion: The mean amount of liquid is NOT less than 7.75 ounces.
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