Evaluate 4a + 7b + 3a − 2b for a = 5 and b = −3.

5) In a certain supermarket, a sample of 60 customers who used a self-service checkout lane averaged 5.2 minutes of checkout tim

Ne4ueva [31]

Answer:

$\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643$

$S_p=2.940$

$t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751$

$df=60+72-2=130$

$p_v =P(t_{130}$

Assuming a significance level of $\alpha=0.05$ we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

Step-by-step explanation:

Data given

Our notation on this case :

$n_1 =60$ represent the sample size for people who used a self service

$n_2 =72$ represent the sample size for people who used a cashier

$\bar X_1 =5.2$ represent the sample mean for people who used a self service

$\bar X_2 =6.1$ represent the sample mean people who used a cashier

$s_1=3.1$ represent the sample standard deviation for people who used a self service

$s_2=2.8$ represent the sample standard deviation for people who used a cashier

Assumptions

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

The statistic is given by:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

And t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

System of hypothesis

Null hypothesis: $\mu_1 \geq \mu_2$

Alternative hypothesis: $\mu_1 < \mu_2$

This system is equivalent to:

Null hypothesis: $\mu_1 - \mu_2 \geq 0$

Alternative hypothesis: $\mu_1 -\mu_2 < 0$

We can find the pooled variance:

$\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643$

And the deviation would be just the square root of the variance:

$S_p=2.940$

The statistic is given by:

$t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751$

The degrees of freedom are given by:

$df=60+72-2=130$

And now we can calculate the p value with:

$p_v =P(t_{130}$

Assuming a significance level of $\alpha=0.05$ we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

5 0

3 years ago

Samantha needs to bake at least 120 pot pies to sell at her restaurant. she can bake 12 pot pies per hour and 15 veggie pot pies

Veronika [31]

Answer:

y>(line under >) - 4/5x + 8

Step-by-step explanation:

Phrase "at least" indicates that the total number of pies is greater than or equal to 120.

The number of chicken pot pies Samantha makes is 12x, and the number of veggie pot pies she makes is 15y.

Use this information to create the inequality:

12x + 15y >(line under >) 120

Simplify by solving for y to get this inequality:

y >(line under >) - 4/5x + 8

3 0

3 years ago

Neil mixes 110 liter of red paint with 310 liter of yellow paint. How many liters of paint does Neil have after mixing the paint

Zolol [24]

Answer:

He has 420 liters of paint.

Step-by-step explanation:

all you have to do is add 110 = 310

5 0

3 years ago

Equation for line passing through (4,3) perpendicular to y=5x+4

ehidna [41]

Perpendicular to the line y = 5x - 9

m= -1/5

the line passing through the point (1, 4):

4=-1/5*1+q
q= 21/5

the equation is:
y= -1/5x +21/5
or
x+5y-21=0

5 0

4 years ago

If you roll a standard 6 sided die, whats the probability that you get a 1,2,3,5, or 6?

Papessa [141]

Answer:

5/6

Step-by-step explanation:

1 has a 1/6 chance
2 has a 1/6 chance
3 has a 1/6 chance
5 has a 1/6 chance
6 has a 1/6 chance
1, 2, 3, 5, or 6 has a 1/6+1/6+1/6+1/6+1/6=5/6 chance

6 0

3 years ago

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