Consider the following hypotheses: H0: p ≥ 0.48 HA: p < 0.48 Which of the following...

Consider the following hypotheses:

H₀: p ≥ 0.48

H_A: p < 0.48

Which of the following sample information enables us to reject the null hypothesis at α = 0.01 and at α = 0.05? (You may find it useful to reference the appropriate table: z table or t table) (Round all intermediate calculations to at least 4 decimal places.)

		α = 0.01		α = 0.05
a.	x = 32; n = 89		(Click to select) Do not reject H0 Reject H0		(Click to select) Do not reject H0 Reject H0
b.	x = 123; n = 323		(Click to select) Reject H0 Do not reject H0		(Click to select) Reject H0 Do not reject H0
c.	p¯ = 0.46; n = 69		(Click to select) Do not reject H0 Reject H0		(Click to select) Do not reject H0 Reject H0
d.	p¯ = 0.46; n = 458		(Click to select) Do not reject H0 Reject H0		(Click to select) Reject H0 Do not reject H0

Solutions

Expert Solution

Since we are comparing sample proportion with the hypothesized proportion, option (a) and (b) are incorrect.

taking option c)

The z-statistic is computed as follows,

The p-value is obtained from the z distribution table for z = -0.3325. (In excel use function =NORM.S.DIST(-0.3325,TRUE)

taking option d)

The z-statistic is,

The p-value is obtained from the z distribution table for z = -0.8567. (In excel use function =NORM.S.DIST(-0.8567,TRUE)

No sample information enables us to reject the null hypothesis at alpha = 0.05 and alpha = 0.01

orchestra answered 1 year ago

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