Problem #1
Null hypothesis: There is no significant difference in the average achievement scores between Preschool and No-Preschool groups.
Alternative hypothesis: There is a significant difference in the average achievement scores between Preschool and No-Preschool groups.
H0: μ1=μ2Ha: μ1≠μ2
Calculate the results for independent samples t-test:
Problem #2
Null hypothesis: There is no significant difference in the performance of sales representatives between 1st month and 6th month groups.
Alternative hypothesis: The performance of sales representatives in 1st month is significantly less than in 6th month.
H0: μ1=μ2Ha: μ1<μ2
The paired t-test should be used:
t=dnd2-d2n-1
t=1.533
The critical t-value for 5% level of significance is 2.132.
The paired t-test indicated that there is no significant difference in the performance of sales representatives between 1st month and 6th month groups (t=1.533, one-tailed p=0.1). We failed to reject the null hypothesis at the 5% level of significance.
Problem #3
Null hypothesis: The average wage in State B is not significantly different from $12.50 per hour.
Alternative hypothesis: The average wage in State B is significantly different from $12.50 per hour.
H0: μ=12.5Ha: μ≠12.5
The critical value of t-test is t(3, 0.05)=3.182.
The t-statistics is:
t=x-μsn=
x=8+8+16+84=10s=13(8-102+8-102+16-102+8-102)=4
t=10-12.542=-1.25
The absolute value of t-statistics is less than the critical value of t. The one-sample t-test indicates that the average wage in State B is not significantly different from $12.50 per hour (t=-1.25). We failed to reject the null hypothesis at the 5% level of significance.
Problem #4
Null hypothesis: There is no significant difference in reading scores between TV watching group and Reading Program group.
Alternative hypothesis: The average reading score in TV Watching group is significantly higher than in Reading Program group.
H0: μ1=μ2Ha: μ1<μ2
Independent samples t-test indicated that there is no significant difference in reading scores between TV watching group and Reading Program group (t=-1.429, p=0.1015). We failed to reject the null hypothesis at the 5% level of significance. The t-value is not significant.
