Question

1. A researcher estimates that the average revenue of the largest businesses in the U.S. is greater than $24 billion. A random sample of 50 companies is selected, and the revenues in billions of dollars are recorded. Assume a Normal distribution with a standard deviation of $30 billion. Is there enough evidence at an 8% level of significance to support the researcher’s claim?

178	30	91	44	35	61	56	46	20	32	41	38	36	15	25	31	30	19	19	19	24	16	15	15	19
122	28	28	20	27	29	16	16	19	15	25	25	18	14	15	24	23	17	17	22	22	21	20	17	20

1. Identify the proper Test or Confidence interval:

2. Complete the Test or Confidence Interval.

Answer 1

n=50,  = 24,   = 0.08

= 31.5 , =30

a)

Here we know the population standard deviation ( )

hence, we are using Z Test

b)

null and alternative hypothesis is

Ho:   24

H1:   > 24

formula for test statistics is

z = 1.77

test statistics= 1.77

c)

calculate P-Value

P-Value = 1 - P(z < 1.77)

using normal z table we get

P(z < 1.77) = 0.9616

P-Value = 1 - 0.9616

P-Value = 0.0384

d)

decision rule is

Reject Ho if ( P-value ) < ( )

here, ( P-value= 0.0384 ) < ( = 0.08 )

Hence, we can say,

Null hypothesis is rejected.

There is sufficient evidence to support the researcher’s claim at 0.08 level of significance.