Question

An article in the San Jose Mercury News stated that students in the California state university system take 5 years, on average, to finish their undergraduate degrees. A freshman student believes that the mean time is less and conducts a survey of 38 students. The student obtains a sample mean of 6.1 with a sample standard deviation of 1.5. Is there sufficient evidence to support the student's claim at an α=0.01α=0.01 significance level?

Determine the null and alternative hypotheses. Enter correct symbol and value.

1) H0: μ= ?????

2) Ha: μ < ?????

3) Determine the test statistic. Round to four decimal places.
t= ??????

4) Find the p-value. Round to 4 decimals.
p-value = ???????

Answer 1

## Q ) An article in the San Jose Mercury News stated that students in the California state university system take 5 years, on average, to finish their undergraduate degrees. A freshman student believes that the mean time is less and conducts a survey of 38 students. The student obtains a sample mean of 6.1 with a sample standard deviation of 1.5. Is there sufficient evidence to support the student's claim at an α=0.01α=0.01 significance level?

Answer : we have given :

n = sample size = 38

xbar = sample mean = 6.1

s = sample standard deviation = 1.5

μ = population mean = 5

α = 0.01 level of significance .

A freshman student believes that the mean time is less than 5

Is there sufficient evidence to support the student's claim at an α=0.01 significance level?

## Determine the null and alternative hypotheses. Enter correct symbol and value.

1) H0: μ= 5

2) Ha: μ < 5

3) Determine the test statistic. Round to four decimal places.
t = (xbar -   μ) *sqrt (n) / s

= ( 6.1 - 5 ) * sqrt(38) / 1.5

= 4.520570 ie

= 4.5206

4) Find the p-value. Round to 4 decimals.

df = n -1 = 37

now use statistical table for p value

p-value = 0.000031 ie

= 0.0000

Decision : we reject Ho if p value is less than  α value using p value approach here p value is less than alpha value we reject Ho

Conclusion : There is sufficient evidence to conclude that there is

sufficient evidence to support the student's claim at an α=0.01 significance level.