Question

Here are some prices for randomly selected grocery items from the grocery store:

Items Prices:

Cheese $3.29

Butter $4.99

Eggs $3.49

Yogurt $3.49

Juice $3.89

Tea $3.69

Chips $3.99

Soda $1.99

Pastry $2.99

Cerrial $4.99

Oats $3.29

Almond Milk $2.79

Almonds $4.39

Popcorn $3.29

Crackers $3.59

Ice Cream $6.99

Cookies $2.99

Jam $3.69

Peanut Butter $3.29

Coffee $3.19

Green Tea $4.99

BBQ Sauce $2.99

Oil $6.69

Mayonnaise $4.59

Mustard $2.99

1. Compute the sample mean x and the sample standard deviation of grocery store prices.

2. State the population mean µx and population standard deviation σx of sample mean in terms of population mean and population standard deviation for the original variable x.

3. Construct the 95% confidence interval for the mean grocery prices. Standard deviation $1.10  

4. Compute the minimum sample size required to have margin of error at most $ 0.30, while keeping the confidence level at 95%. Standard Deviation is $1.10

5. Construct the 95% confidence interval for the mean grocery store prices. (This time assume that the standard deviation σx is unknown).

6. Suppose the mean grocery price for Safeway is known to be $ 4.10. Test the hypothesis that the mean grocery price for this grocery store vs from mean another grocery stores price with significance level α = 0.10. Standard deviation is $1.10

7. Retest the hypothesis that the mean grocery price for this grocery store vs mean another grocery stores price at significance level α = 0.10. (This time, assume that the standard deviation σx is unknown).

This is for the purposes of checking answers and comparing work. Thank you.

Answer 1

1. Sample mean=$4.13, Sample standard deviation=$1.37.

2.