Question

When carrying out hypothesis testing using statistical methods, we are trying to infer something about what’s going on in a population, based on what’s going on in a random sample from that population. If we want to learn about the population mean annual spending by households on video games, describe a hypothesis testing procedure for testing the hypothesis that this spending level equals 100 dollars.

Answer 1

Here, we have to discuss the hypothesis procedure for checking the claim regarding the mean annual spending by households on video games. First of all, we need to find proper test for checking the claim. Here, we will use one sample t test for the population mean if we don’t know the population standard deviation. If we know the population standard deviation and sample size is adequate then we will use one sample z test instead of t test. it is important to check the assumptions required for conduction of hypothesis test. We will select the random sample from normally distributed population. We will collect the sample data for at least 30 households expenditure on video games. Then we will find out the sample mean and sample standard deviation for this collected data. The null and alternative hypothesis for this test will be given as below:

Null hypothesis: H₀: The average annual spending by households on video games is $100.

Alternative hypothesis: H_a: The average annual spending by households on video games is more than $100.

(You can change the alternative hypothesis as per situation.)

H₀: µ = 100 versus H_a: µ > 100

Then we will find the test statistic value by using the following formula:

t = (Xbar - µ)/[S/sqrt(n)]

Where, Xbar is sample mean, S is sample standard deviation, n is sample size.

We will find these values by using collected data for random sample. We will assume 5% level of significance for this test.

After finding test statistic value, we will find critical value or p-value for this test by using t-table.

We will take decision regarding null hypothesis based on the comparison of either critical value and test statistic or p-value and alpha value for this test.

Finally we will write the conclusion regarding the claim defined for this test.