Question

According to a survey, the average American person watches TV for 3 hours per week. To test if the amount of TV in New York City is less than the national average, a researcher decides to do a hypothesis test, at a 10% significance level. She surveys 26 New Yorkers randomly and asks them about their amount of TV each week, on average. From the data, the sample mean time is 2.5 hours per week, and the sample standard deviation (s) is 1.1 hours. H0: μ≥3; Ha: μ<3. α=0.1 (significance level) What is the test statistic (t-value) of this one-mean hypothesis test (with σ unknown)? Round your final answer to two decimal places. Provide your answer below:

Answer 1

-1.32

Explanation:

Since we want to test if
`\bf \mu` of the alternative hypothesis is less than the established in the null, this is a left-tailed test.

At 10% significance level the t-statistic (t-value) is the value of t such that the area under the Student's t-distribution curve with 25 degrees of freedom (sample size -1) to the left of t equals 10% = 0.1

Either by using a table or the computer, we find

`\bf t= -1.316\approx -1.32`

Answer 2

t=2.32

Explanation:

t-value= (population mean-sample mean)/√ (sample SD²/sample size)

t= (3-2.5)/√(1.1²/26)