Question

1. A grocery store gave people the choice for a free sample of chocolate-chip brownies or chocolate-chip cake. They were told they were only allowed to pick one of the two samples and their choices were recorded.The statistic observers ensured that the samples were plentiful to prevent people from feeling bad for taking all of one sample or the other. Over the course of 325 customers, 210 chose the chocolate-chip brownies.

a) Can we perform a statistical study based on this sample?

b) Create a Hypothesis Test for the importance of chocolate-chip brownies over cake.

c) Estimate the standard error for this study. Round to three decimal places.

d) Find the test statistic for your study. Round to three decimal places.

e) Find the p-value.

f) Do we have enough evidence that people prefer chocolate-chip brownies over cake?

2.  A community university wants to suggest its students have all scored over 500 on their SAT English scores each year. Gathering 40 random students from the past 10 years, the average score per year is 520 with a standard deviation of 110.

a) Is this sample appropriate for a normalized confidence interval?

b) Find the standard error for this sample.

c) Find the appropriate t-distribution for the 95% confidence interval.

d) Find the confidence interval based on the sample.

e) Based on your confidence interval, is the university allowed to brag about its high SAT English scores?  Why or why not?

Answer 1

1. a) To study whether interest of people on the chocolate-chip brownies or chocolate-chip cake

b) H0: the importance of chocolate-chip brownies not over cake

H1: the importance of chocolate-chip brownies over cake

c)

e) P-Value:           0.0000

f) Since P-value < alpha 0.05, so we reject H0

Thus we conclude that the importance of chocolate-chip brownies over cake

----------------------------------------------------------------------------------------------------------------------------------------------------------------------

2)

a) Yes, the sample appropriate for a nomalized confidence interval
since sample size n = 40 which is >30 (large)

All large sample follows normal distribution

b) Standard error = SD / Sqrt(n)
                  = 110 / sqrt(40)
                  = 17.3925

c) Confidence interval:

d) The confidence interval from the sample is 484.82 and 555.18

e) No, The university allowed to brag about its not high SAT English scores

since The value 500 is contained in the confidence interval