17. A study was conducted to compare two reading intervention programs and evaluate whether they are equally effective with regard to improving reading proficiency. Ten students are recruited; five are randomly assigned to the new program and the remaining five are assigned to the standard program. Two months after being enrolled in the program, reading proficiency of the students is evaluated using a reading test. Output from the R function, inference, is shown below for the comparison of the test scores for students in the two programs. Use this output and a significance level of 0.01 to answer the following question.

Summary statistics:

n_New = 5, mean_New = 85.8, sd_New = 6.3797

n_Standard = 5, mean_Standard = 72.6, sd_Standard = 7.0922

Observed difference between means (New-Standard) = 13.2

H0: mu_New - mu_Standard = 0

HA: mu_New - mu_Standard != 0

Standard error = 4.266

Test statistic: T = 3.094

Degrees of freedom: 4

p-value = 0.0364

Based on the above output, we test whether there is a significant difference in reading proficiency score for students in the two reading intervention programs. The conclusion is:

Group of answer choices

Fail to reject H0. There is insufficient statistical evidence to say that there is a difference in the average reading proficiency for students in the two reading programs.

Reject H0. There is insufficient statistical evidence to say that there is a difference in the average reading proficiency for students in the two reading programs.

Reject H0. There is sufficient statistical evidence of a difference in the average reading proficiency for students in the two reading programs.

Fail to reject H0. There is sufficient statistical evidence of a difference in the average reading proficiency for students in the two reading programs.