Question

A recent broadcast of a television show had a 10 share, meaning that among 6000 monitored households with TV sets in​ use, 10​% of them were tuned to this program. Use a 0.01 significance level to test the claim of an advertiser that among the households with TV sets in​ use, less than 15​% were tuned into the program. Use the​ P-value method. Use the normal distribution as anapproximation of the binomial distribution

A) Identify the null​ hypothesis, and alternative​ hypothesis

B) test​ statistic z= (round to nearest 2 decimal places)

C) P-value (4 decimal places)

D) make a conclusion about the null​ hypothesis (reject or fail to reject, is or is not sufficeint evedince to support the claim of 15%)

Answer 1

Given,

6000 monitored households with TV sets in​ use, 10​% of them were tuned to this program

claim of an advertiser that among the households with TV sets in​ use, less than 15​% were tuned into the program

A) Hypothesied proportion : = 15/100 = 0.15

Null hypothesis : Ho :

Alternate hypothesis : Ha : ( Left Tailed test)

B)

Given
Hypothesied Proportion :	0.15
Sample Size	6000

Sample proportion = 10/100 = 0.1

Level of significance = 0.01

Z = - 10.8465

p-value

C)

D)

As P-Value i.e. is less than Level of significance i.e (P-value:0 < 0.01:Level of significance); Reject Null Hypothesis

is sufficient evedince to support the claim of 15%

Using Excel Function to find the P-value : NORM.S.DIST functionNORM.S.DIST function

Returns the standard normal distribution (has a mean of zero and a standard deviation of one).
Use this function in place of a table of standard normal curve areas.Syntax – Standard Normal DistributionNORM.S.DIST(z,cumulative)
The NORM.S.DIST function syntax has the following arguments:
## Z Required. The value for which you want the distribution.
## Cumulative Required. Cumulative is a logical value that determines the form of the function. If cumulative is TRUE, NORMS.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.