Q1) The director is considering introducing new packaging for an existing product. Two styles of packaging, X and Y, were proposed. The company decided to try the new packaging in a random sample of shops. The sample sizes and the results are given below: Packaging X Packaging Y Sample size 60 50 Mean sales 280 300 Standard deviation of sales 50 70 (a) Test, at the 0.05 level of significance, whether the sales for the product with Y packaging were significantly higher than that for the product with X packaging. (b) Compute the p-value and indicate whether it leads to the same conclusion.

An industrial plant wants to determine which of two types of fuel, electric or gas, is more cost efficient (measured in cost per unit of energy). Independent random samples were taken of plants using electricity and plants using gas. These samples consisted of 14 plants using electricity, which had a mean cost per unit of $55.06 and standard deviation of $8.25, and 12 plants using gas, which had a mean of $57.80 and standard deviation of $7.81. Assume that the populations of costs per unit are normally distributed for each type of fuel, and assume that the variances of these populations are equal. Can we conclude, at the 0.10 level of significance, that μ₁, the mean cost per unit for plants using electricity, differs from μ₂, the mean cost per unit for plants using gas? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of…

The void volume within a textile fabric affects comfort, flammability, and insulation properties. Permeability of a fabric refers to the accessibility of void space to the flow of a gas or liquid. An article gave summary information on air permeability (cm3/cm2/sec) for a number of different fabric types. Consider the following data on two different types of plain-weave fabric: Fabric Type Sample Size Sample Mean Sample Standard Deviation Cotton 10 51.41     0.75 Triacetate 10 132.15     3.59 Assuming that the porosity distributions for both types of fabric are normal, let's calculate a confidence interval for the difference between true average porosity for the cotton fabric and that for the acetate fabric, using a 95% confidence level. Before the appropriate t critical value can be selected, df must be determined: df =    0.5625 10  +  12.8881 10   2   (0.5625/10)2 9  +  (12.8881/10)2 9  =  1.8092 0.1849…

You are a researcher assessing self-checkout lane violations at supermarkets in a town in the southern United States. The supermarket has five (5) self-checkout lanes. The violations by each lane are as follows: Lane A: 5 violations Lane B: 10 violations Lane C: 15 violations Lane D: 20 violations Lane E: 25 violations Please calculate the following (your standard deviation is 7.91): Mean:  Standard Error of the Mean:  Please interpret your Standard Error of the Mean.

An industrial plant wants to determine which of two types of fuel, electric or gas, is more cost efficient (measured in cost per unit of energy). Independent random samples were taken of plants using electricity and plants using gas. These samples consisted of  9  plants using electricity, which had a mean cost per unit of  $51.9  and standard deviation of  $7.98 , and  14  plants using gas, which had a mean of  $55.5  and standard deviation of  $8.73  . Assume that the populations of costs per unit are normally distributed for each type of fuel, and assume that the variances of these populations are equal. Can we conclude, at the  0.05  level of significance, that the mean cost per unit for plants using electricity,  μ1 , differs from the mean cost per unit for plants using gas,  μ2 ? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If…