Question

Due to distance learning and less homework load in Peach Elementary School, parents are complaining that the average screen time is more than 3 hours per day for students in Grade 1 to Grade 3. The principal randomly selected 36 students from Grade 1 - Grade 3 and statistical summary is shown below.

min	avg	max	std
3	5	8	2.5

a. Write the hypothesis in symbols or words

b. Check the two conditions for CLT.

c. Calculate the test statistics and the associated degrees of freedom

d. Use the p-value or critical value approach to make your conclusion at 5% significance level.

one tail (upper)	0.1	0.05	0.025	0.01	0.005
two tails	0.2	0.1	0.05	0.02	0.01
t value, df = 35	1.31	1.69	2.03	2.44	2.73

Answer 1

Solution:

Given that

n= 36 sample size

population mean

sample mean

s = 2.5 sample standard deviations

level of significance

a) To test the hypothesis

. Vs.

Hypothesis in words

Ho: The average screen time is same 3 hours per day for students in grade1 to grade 3.

Vs

Ha: The average screen time is more than 3 hours per day for students in grade1 to grade 3

b) Condition for CLT

1) The sample observation of grade 1 to grade 3 students are independent to each other.

2) The sample is drawn without replacement of the grede 1 to grade 3 students.

3) sample size of grade 1 to grade 3 students not more than 10% of the population.

c) Test statistic

t = 4.8000007

Test statistic t = 4.8000

The degree of freedom associated with the test statistic is n-1 =36-1=35

The degree of freedom =35

The t critical value at is

from t table

The t critical value =1.69

d) Decision :

t stat > t critical value

4.80 > 1.69

Reject Ho

Conclusion: Reject Ho, there is sufficient evidence to conclude that the average screen time is more than 3 hours per day for students in grade1 to grade 3.