The number of entrees purchased in a single order at a Noodles & Company restaurant has had an historical average of 1.7 entrees per order. On a particular Saturday afternoon, a random sample of 48 Noodles orders had a mean number of entrees equal to 2.1 with a standard deviation equal to 1.01. At the 2 percent level of significance, does this sample show that the average number of entrees per order was greater than expected?

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean is higher than 1,7 entrees per order at 2% of signficance.  

Step-by-step explanation:

Data given and notation  

represent the mean

represent the sample standard deviation

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 1.7, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

 (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

P-value

The first step is calculate the degrees of freedom, on this case:  

Since is a one side test the p value would be:  

Conclusion  

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean is higher than 1,7 entrees per order at 2% of signficance.  

The unit cell edge length for the alloy is 0.405 nm

Explanation:

Given;

concentration of Ag, = 78 wt%

concentration of Pd, = 22 wt%

density of Ag = 10.49 g/cm³

density of Pd = 12.02 g/cm³

atomic weight of Ag, = 107.87 g/mol

atomic weight of iron, = 106.4 g/mol

Step 1: determine the average density of the alloy

Step 2: determine the average atomic weight of the alloy

Step 3: determine unit cell volume

for a FCC crystal structure, there are 4 atoms per unit cell; n = 4

Step 4: determine the unit cell edge length

Vc = a³

= 0.405 nm

Therefore, the unit cell edge length for the alloy is 0.405 nm