Annual per capita consumption of milk is 21.6 gallons ( Statistical Abstract of

Question

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the mid western town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of s = 4.8.

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: (greater than 21.6) (greater than or equal to 21.6) (equal to 21.6less than or equal to 21.6) (less than 21.6) (not equal to 21.6)
Ha: (greater than 21.6) (greater than or equal to 21.6) (equal to 21.6less than or equal to 21.6) (less than 21.6) (not equal to 21.6)

Explanation / Answer

Null and Alternative Hypothesis:

H0: less than or equal to 21.6

Ha: greater than 21.6

Or

H0: µ 21.6

Ha: µ > 21.6

Level of significance:

Alpha = .05

Test Statistics:

t = ( x bar - µ) / ( s / sqrt (n))

= (24.1 – 21.6) /(4.8/sqrt(16))

= 2.083

Decision:

The null hypothesis can be rejected if the value of the test statistics is greater than the critical t.

For 15 degrees of at 5% level of significance we get the critical t from t-table as 1.753

The test value 2.083 is greater than 1.753; the null hypothesis can be rejected.

Conclusion: There is sufficient evidence to conclude that the mean annual consumption in Webster City is higher than the national mean.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.