In Hamilton County, Ohio the mean number of days needed to sell a home is 86 days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of 40 homes in a nearby county showed a sample mean of 80 days with a sample standard deviation of 20 days. Conduct a hypotheses test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county. Round your answer to four decimal places.

Test statistic is -1.8975

The mean number of days until a home is sold is not different than the Hamilton county mean of 86 days in the nearby county.

Step-by-step explanation:

Null hypothesis: The mean number of days until a home is sold in the nearby county is the same as Hamilton county.

Alternate hypothesis: The mean number of days until a home is sold in the nearby county is different from Hamilton county.

Z = (sample mean - population mean) ÷ sd/√n

sample mean = 80 days

population mean = 86 days

sd = 20 days

n = 40

Z = (80 - 86) ÷ 20/√40 = -6 ÷ 3.162 = -1.8975

Assuming a 0.05 significance level, the critical value for a two-tailed test lies between -1.96 and 1.96

Conclusion: Since the test statistic -1.8975 falls within the region bounded by -1.96 and 1.96, fail to reject the null hypothesis

1; 35 is the ratio

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .