Question

Select the null and the alternative hypotheses for the following tests:

a. Test if the mean weight of cereal in a cereal box differs from 18 ounces.
O H0: μ = 18; HA: μ ≠ 18
O H0: μ ≥ 18; HA: μ < 18
O H0: μ ≤ 18; HA: μ > 18
b. Test if the stock price increases on more than 60% of the trading days.
O H0: p ≤ 0.60; HA: p > 0.60
O H0: p ≥ 0.60; HA: p < 0.60
O H0: p = 0.60; HA: p ≠ 0.60
c. Test if Americans get an average of less than seven hours of sleep.
O H0: μ ≥ 7; HA: μ < 7
O H0: μ ≤ 7; HA: μ > 7
O H0: μ = 7; HA: μ ≠ 7

Answer 1

Option A)

`H_(0): \mu = 18\text{ ounces}\\H_A: \mu \\eq 18\text{ ounces}`

Option A)

`H_(0): p \leq 0.6\\H_A: p > 0.6`

Option A)

`H_(0): \mu \geq 7\text{ hours}\\H_A: \mu \leq 7\text{ hours}`

Explanation:

We have to design null and alternate hypothesis for given test:

a) Test if the mean weight of cereal in a cereal box differs from 18 ounces.

Option A)

`H_(0): \mu = 18\text{ ounces}\\H_A: \mu \\eq 18\text{ ounces}`

The null hypothesis means mean cereal box weight is 18 ounces and the alternate hypothesis state that it is different than 18 ounces.

b) Test if the stock price increases on more than 60% of the trading days.

Option A)

`H_(0): p \leq 0.6\\H_A: p > 0.6`

The null hypothesis states that the proportion is less than 0.6 that is stock price is less than or equal to 60% of the trading days and alternate hypothesis states that the proportion is greater than 0.6 that is stock price increases on more than 60% of the trading days.

c) Test if Americans get an average of less than seven hours of sleep.

Option A)

`H_(0): \mu \geq 7\text{ hours}\\H_A: \mu \leq 7\text{ hours}`

The null hypothesis states that the Americans get an average of greater than or equal to 7 hours of sleep where as the alternate hypothesis states that the Americans get a sleep less than 7 hours of sleep.