Question

Consider the following hypotheses:

H₀: μ = 1,800
H_A: μ ≠ 1,800

The population is normally distributed with a population standard deviation of 440. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can "reject/do not reject" the null hypothesis at the 10% significance level. (You may find it useful to reference the appropriate table: z table or t table) (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round "test statistic" values to 2 decimal places and "p-value" to 4 decimal places.)

		Test statistic	p-value
a.	x−x− = 1,850; n = 110			(Click to select)  Reject H0  Do not reject H0
b.	x−x− = 1,850; n = 280			(Click to select)  Reject H0  Do not reject H0
c.	x−x− = 1,650; n = 32			(Click to select)  Reject H0  Do not reject H0
d.	x−x− = 1,700; n = 32			(Click to select)  Reject H0  Do not reject H0

Answer 1

Solution :

= 1800

= 440

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 1800

H_a :     1800

= 0.05

					Test statistic z	p-value
	a		x -x=1850,n =110		Test statistic = z = ( - ) / / n = (1850-1800) /440 / 110 =1.19	0.2333	Do not reject H0
	b		x-x =1850 ,n =280		= ( - ) / / n = (1850-1800) /440 / 280 =1.90	0.0572	Reject H0
	c		x-x =1650, n =32		= ( - ) / / n = (1650-1800) /440 / 32 = -1.93	0.0538	Reject H0
	d		x-x =1700 , n= 32		= ( - ) / / n = (1700-1800) /440 / 32 = -1.29	0.1986	Do not reject H0