Question

According to a recent study annual per capita consumption of milk in the United States is 21.5 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption below.

Gallons of Milk

27.1

23.84

25.25

21

17.52

19.61

19.83

26.18

34.97

29.9

28.59

20.57

26.94

27.24

Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean.

H₀: ? _________

H_a: ? _________

What is a point estimate of the difference between mean annual consumption in Webster City and the national mean? ____________(2 decimals)

At ? = 0.01, test for a significant difference by completing the following.

Calculate the value of the test statistic ________________(2 decimals).

The p-value is ____________ (4 decimals)

Reject the null hypothesis? No or Yes

What is your conclusion?

There is insufficient evidence to conclude that the population mean consumption of milk in Webster City is greater than the hypothesized mean.

or

Conclude the population mean consumption of milk in Webster City is greater than the hypothesized mean.

Answer 1

Given: Population mean (µ) = 21.5 .

The claim statement is, "The mean annual consumption in Webster City is higher than the national mean".

That is µ > 21.5.

Hence, the claim statement goes under the alternative hypothesis.

Hence, the Null hypothesis is, H0: µ <= 21.5

And the alternative hypothesis is, H1: µ > 21.5

Now, we need to find the sample mean and sample standard deviation by using the given data.

You can calculate the mean and standard deviation using technology.

Sample mean = xbar = 24.89571.

Sample standard deviation = S = 4.799798

Next part: What is a point estimate of the difference between mean annual consumption in Webster City and the national mean?

The point estimate of the difference = xbar - µ = 24.89571 - 21.5 = 3.39571

After rounding it to two decimal places, we will get a point estimate of the difference = 3.40

Here, we have the sample standard deviation. So, we need to use the T-test for testing.

Now, let's find the test statistic.

Plug the values in this formula.

We will get, T = 2.647111

After rounding to two decimal places, we will get, T = 2.65

Degrees of freedom = n-1 = 14 - 1 = 13 .

Now, let's find the P-value.

For finding the P-value, we can use a technology like excel/Ti84 calculator or T table.

The following excel command is used to find the P-value.

= 1 - T.DIST(Test statistic, Degrees of freedom, 1)

= 1 - T.DIST(2.647111 , 13 , 1)

You will get, Critical T value = 0.01006

After rounding it to four decimal places, we will get P-value = 0.0101

We are given α = 0.01

Following is the decision rule for making the decision.

If, P-value > α, then we fail to reject the null hypothesis.

If, P-value <= α, then we reject the null hypothesis.

Here, given α = 0.01

And P-value = 0.0101

That is P-value = α.

Hence, we reject the null hypothesis.

That is, accepting the alternative hypothesis.

There is insufficient evidence to conclude that the population mean consumption of milk in Webster City is greater than the hypothesized mean.