Question

4. The production line for Glow toothpaste is designed to fill tubes with a mean weight of 6 oz. Periodically, a sample of 35 tubes will be selected in order to check the filling process. Quality assurance procedures call for the continuation of the filling weight for the population of toothpaste tubes is 6 ounces; otherwise the processes will be adjusted. Suppose a sample of 35 toothpaste tubes provides a sample mean of 6.1 oz and standard deviation of 0.2 oz. Perform a hypothesis test, at 0.03 level of significance, to help determine whether the filling process should continue operating or be stopped and corrected.

Answer 1

Answer)

Ho(null hypothesis) : mean = 6

Ha (alternate hypothesis) : mean is not equal to 6

As here population standard deviation is known 0.2

Therefore we will use z test

(In case sample standard deviation is given instead of population standard deviation, then we use t test)

Z = (sample mean - population mean)/(standard deviation/√n)

Sample mean = 6.1

Population mean = 6

Standard deviation = 0.2

N = 35

Z = (0.1)/(0.2/√35)

= 2.95803989154

Now we need to look in to the z table for 2.96

= 0.9985

Now we know that z table show the value of p(z<2.96)

And as this is two tailed test (as here we are given with not equal to sign, in case of greater than or less than, we use one tail)

So we need to subtract 0.9985 from 1 in order to get the value of one tail

= 1-0.9985

Now we need to multiply it with 2, to get the value of both the tails

= 2*(1-0.9985)

P-value = 0.003

As the p-value is less than alpha(0.03)

We reject the null hypothesis

As the null hypothesis is rejected

So, the process should be stopped and corrected.