(c) Find the regression equation for the given data (An immediate equation by a calculator will be considered wrong! Show all the details to justifier your answer). ( d) Give an estimation of y if x = 7. 76.

3. A random sample of 157 people asked about their ice cream flavour preferences (Chocolate, vanilla, and strawberry). The results are shown in the following contingency table. Chocolate Vanilla Strawberry Female 40 27 Male 16 35 (a) Complete the following table Cell Observed Frequency 0 Expected Frequency E (0-E Celll 40 Cell2 27 Cell3 15 Cell4 16 Cell5 35 Cell6 24 Sum 157 15 24 E)2

(b) Use a 1 % significance level to test the claim that there is dependence between gender and preference for ice cream flavour.

4. Listed below is a sequence of 25 items, called H (high) and L (low): HH LLL HH LL HH LLL HH LLLL We wish to use the runs test for randomness with a 0.01 significance level to test whether above sequence was produced in a random manner. (a) Write the null hypothesis Ho and alternative hypothesis (b) Compute the value of the appropriate test statistic. HHH LL the H1.

(c) Find the critical value(s), and state the right conclusion about the randomness above sequence. of the

5. A school is selling tickets to a spring musical. On the first day of ticket sales the sold 2 senior citizen tickets and 9 child tickets for a total of $171. The school took in $214 the second day by selling 3 senior citizen tickets and 11 child tickets. Find the price of a senior citizen ticket and the price of a child ticket? (Hint: Write a system of equations that describes the above situation and specify what each variable does represent). school on

6. A psychologist runs a series of experiments with a mouse in a maze containing two rooms. Each time period the doors in the maze are opened, it is allowed to move from one room another room. If the mouse is in the first room, 75% of the time it decides to stay in it. other hand, if it is in the second room, 40% of the time it decides to move to the first room. (a) Write down a transition matrix. (b) If the mouse is now in the first room, what is the probability it will be in room after three time periods? to On the the second