A new weight-loss company,Lose Weight Easily,advertises that those who join their diet program will lose, on average, 4 kilograms in the first two weeks of starting the program. This claim is now under dispute. A random sample of 50 people who joined the weight-loss program revealed that the mean weight loss was 3.6 kilograms in the first two weeks. The amount of weight loss is assumed to be normally distributed with a standard deviation of 1.1 kilograms. Based on this sample, and using a 5% significance level, can we conclude that those joiningLose Weight Easilywill lose less than 4 kilograms in the first two weeks?

Use the following template of thecritical value methodto answer the question.

Use the template of the critical value method to answer the question.

Step 1: Hypotheses (1 mark)

H_o:

H_A:

Step 2: Standardised test statistic formula (Case 1, Case 2 or Case 3) Case 3Case 1Case 2

Step 3:Level of significance =0.05

Step 4 (a) - What tailed test is this (Left tailed, Right tailed or Two-tailed)? Right-tailedTwo-tailedLeft-tailed

Step 4 (b) - What is the Critical value/s? 1.645, 1.676, 1.96, - 1.645, - 1.676, - 1.96 Step 4 (c)- State the decision rule.

Step 5 - Calculation of the test statistic. -2.57, - 18.18, - 1.645, 2.57, 18.18, 1.645

Step 6 - Conclusion

An investment manager is interested in the relationship between stock prices and bond prices. They collected data on the average stock prices (in dollars $) and the average bond prices (in dollars $) over the past ten years. The data collected is shown in the table below.

Assist the manager by performing a simple linear regression analysis on the 2 (two) quantitative variables.

Stock price ($)(x)	58	41	30	59	32	50	16	85	24	67
Bond price ($) ( y )	15	12	18	14	20	12	33	12	18	11

Given thatx_i= 462 y_i= 165 x_i²= 25496 y_i²= 3111 x_iy_i= 6685 n = 10 x = 46.2 y = 16.5

a)ComputeS_x²,S_y²andS_xyusing the information given above.

S_x²= 461.2889, 2827.7556, -18511.5111, 415.16

S_y²= 343.8333, -2376.8333, 43.1667, 38.85

S_xy= -772.7222, -6880.2222, -104.2222, -93.8

b) Compute the sample correlation coefficient using the values calculated in part a).

Correlation Coefficient = -0.7785, 0.7785, -0.7386, -0.0052

c) Provide an interpretation of the value of the correlation coefficient calculated in part b) in terms of the relationship between stock prices and bond prices.

Answer: Interpretation =