Question

7.) The target temperature for a hot beverage the moment it is dispensed from a vending machine is 173◦F. A sample of 15 randomly selected servings from a newly manufactured vending machine gave a mean temperature of 170◦F with a standard deviation of 6.4◦F. Using our 6-step process, test that the mean tem- perature dispensed from this new machine differs from the target temperature.

Answer 1

Solution:

The null and alternative hypothesis are

H₀: = 173 vs H_a:    173

The test statistic t is

t =  

= (170 - 173)/(6.4/15)

= -1.815

Now , df = n - 1 = 15 - 1 = 14

Now, sign in H1 indicates that the two tailed test.

Using t = -1.815 , df = 14 , Two tailed test

p value = 0.091

If we use 0.05 significance level , then we fail to reject the null hypothesis. Because the p value is greater than 0.05

There is not sufficient evidence to conclude that the mean tem- perature dispensed from this new machine differs from the target temperature.

If we use 0.10 significance level , then we reject the null hypothesis. Because the p value is less than 0.05

There is sufficient evidence to conclude that the mean tem- perature dispensed from this new machine differs from the target temperature.