## Related questions with answers

A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.20 cups per day and 1.36 cups per day for those drinking decaffeinated coffee. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.84 cups per day. Use the .01 significance level. Compute the p-value.

Solution

VerifiedGiven:

$\begin{align*} n_1&=\text{Sample size}=50 \\ n_2&=\text{Sample size}=40 \\ \overline{x}_1=&\text{Sample mean}=4.35 \\ \overline{x}_2=&\text{Sample mean}=5.84 \\ \sigma_1&=\text{Population standard deviation}=1.20 \\ \sigma_2&=\text{Population standard deviation}=1.36 \\ \alpha&=\text{Significance level}=0.01 \end{align*}$

Given claim: Mean is less for the regular-coffee drinkers

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis and the alternative hypothesis state the opposite of each other. The null hypothesis needs to include an equality.

$\begin{align*}H_0&:\mu_1\geq \mu_2 \\ H_a&: \mu_1 < \mu_2 \end{align*}$

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