Please answer all questions. Thank you.

The prices per gallon of gas from a random sample of gas stations in Columbia in 2012. A researcher hypothesizes that the mean gas rates in Columbia in 2012 rose above the mean price of $3.57 the previous year (2014). Please show calculation and explanation. level of confidence= 0.05

3.48 3.513.523.533.543.553.563.573.593.613.623.633.653.663.673.69 3.75

1. One tailed or two tailed? Please Write hypothesis. and solve problem depending on either its two tailed or one tailed.
2. State the p-value and interpret in terms of context, not in terms of hypothesis.
3. Calculate a 95% confidence interval and interpret. Please mention critical value and level of confidence that you will use based on one or two tailed test.

A new diet program states that the participants are expected to lose at least 22lbs in 5wks. Suppose that, from the data of the 5wk weight losses of 56 participants, the sample mean and standard deviation are found to be 23.4 and 10.1 lbs respectively. use alpha = 0.01 . Show calculation and explanation.

a. One tailed or two tailed?

b.Find the test statistic.

c.State the p-value and interpret in terms of context , not in terms of null hypothesis.

f.Calculate a 99% confidence interval and interpret.