Question

1. Define how to find different values of r with the correlation coefficient.

2. Suppose the results of a hypothesis test indicate that we should not reject the null hypothesis. according to that result, where should we place the test stat with respect to a one-tail test to the right? Place the stat on the axis for the picture below, and explain the reasoning.

3.a survey of 225 people indicate that 174 of them prefer Jimmy John's to Subway. Construct the 90% interval estimate for the proportion of people that prefer jimmy john's to Subway. Use p+/- E.

Can we conclude from these results that more than 80% of people prefer Jimmy John's to Subway? Explain the reasoning.

Answer 1

Solving the question 3 as the other 2 are incomplete (picture missing)

3)

Given
p̂ = 0.7733           ....... Sample Proportion
n = 225           ....... Sample Size

For 90% Confidence interval

α = 0.1,      α/2 = 0.05
From z tables of Excel function NORM.S.INV(α/2) we find the z value
z = NORM.S.INV(0.05) = 1.645
We take the positive value of z

Confidence interval is given by


= (0.7274, 0.8192)

= (72.74%, 81.92%)    in terms of percentage

90% Confidence interval for population proportion is

The 90% confidence interval indicates that when samples similar to the above are taken and interval calculated, 90% of the intervals will have population proportion between 72.74% and 81.92%

In the interval calculated above, the lower limit is less than 80%.

Thus, there is a chance that less than 80% people may prefer Jimmy John's to Subway

Hence, we cannot conclude from these results that more than 80% of people prefer Jimmy John's to Subway