Question: (26 points) A computer company claims that their new keyboard is designed for faster typing, In a pilot study, six subjects typed the same material on both the new and an old keyboard. Given the scores below (in words per minute), perform a matched t test = 0.05, two tailed),

Subject Old keyboard New keyboard

1. 48 52

2 56 56

3 49 55

4 68 65

5 66 67

6 59 63

(a) State the null hypothesis and alternative hypothesis in mathematical notations.

(b) Find the test statistic t. (Note: You should find \(\bar{D}\) and s_D from the data first.)

(c) Find the p value for a two-tailed test. (Note: You need to use a t-distribution calculator for this.)

(d) For a two-tailed test, with a = 0.05, what are the critical values?

(e) What should the conclusion be given the above results?

(f) If the conclusion above is an error, what type of error would that be?

(g) Repeat the hypothesis test above with \(\alpha =0.01\), find the test statistics, p-value, critical values and state the conclusion.