Null Hypothesis
: The mean increase in height
is greater than or equal to 5.6 inches.
Alternate Hypothesis
: The mean increase in height
is less than 5.6 inches.
Where the above statistical scenario is given, it is to be noted that the hypothesis is a one tailed test.
In this test, we're checking if boys' average height increase between ages 12 and 14 is less than 5.6 inches.
The null hypothesis
assumes the increase is 5.6 inches or more, while the alternate hypothesis
suggests it's less than 5.6 inches.
Hence, the appropriate null and alternate hypotheses for this hypothesis test are:
- Null Hypothesis
: The mean increase in height
is greater than or equal to 5.6 inches.
![\[ H_0: \mu_n \geq 5.6 \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/8919x1norre10sd1p0x5pjuz8nkcwnzj1d.png)
- Alternate Hypothesis
: The mean increase in height
is less than 5.6 inches.
![\[ H_1: \mu_n < 5.6 \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/j2tl3jg2a8c3vhwl6m6gtj7w1svy9ammb7.png)
This hypothesis test is a one-tailed test. This is because we're specifically looking at a reduction in height increase.
Full Question:
Although part of your question is missing, you might be referring to this full question:
Growth spurt: It is generally known that boys grow at an unusually fast rate between the ages of about 12 and 14. Following are heights, in inches of 10 boys, measured at age 12 and again at age 14. Can you conclude that the mean increase in height is less than 5.6 inches? Let u, represent the mean height at age 14 and un = u, -uy. Use the a= 0.05 level and the P-value method with the TI-84 Plus calculator.
Height
Age 12 68.3 63.0 64.4 58.2 59.7 60.2 63.7 60.2 62.7 55.6
Age 14 73.6 67.7 69.2 64.6 66.1 65.9 68.3 65.2 67.9 61.7
(a) State the appropriate null and alternate hypotheses.
:
H1:
This hypothesis test is a _____ test.