An ESL (English as a Second Language) instructor uses a novel technique of teaching English to his students, one he believes will lead to differences in English proficiency level. To evaluate their English proficiency, he administers a standardized test of English proficiency with scores on this test ranging from a minimum of 20 to a maximum of 80. To interpret their performance level on the test, he would like to compare their mean with the hypothesized population mean () = 50. The instructor would like to determine if the mean English test score for the sample ofn = 20 students is different from the population mean, = 50. Use = .05.

a. ) State the null and alternative hypotheses (H₀& H₁) using statistical notation

b.) What are the degrees of freedom? Show your calculation.