A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be ¯ x = $ 14.50 . Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is σ = $ 3.50 . To address the CEO’s conjecture, the marketing manager decides to carry out a test of hypothesis. The null hypothesis is given by H 0 : μ = 13.50 . The hypothesis test is set up to provide the marketing manager with: evidence against the null hypothesis in favor of the alternative. evidence in favor of the null hypothesis. proof that the null hypothesis is true. evidence against the alternative hypothesis in favor of the null hypothesis.

t = 1.399<1.710 ( from tabulated value)

we will accepted the null hypothesis

the marketing manager decides to carry out a test of hypothesis

H 0 : μ = 13.50

Step-by-step explanation:

Step1 :-

Given sample size 'n' = 25 customers

The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch.

therefore the population mean 'μ' = $13.50

A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be ¯ x = $ 14.50

sample mean ¯ x = $ 14.50

the restaurant informs the marketing manager that the standard deviation is σ = $ 3.50

Population standard deviation σ = $ 3.50

Step 2:-

we will use' t' test because of given small sample size is n=25

Null hypothesis: H₀ : μ= $ 13.50

Alternative hypothesis :H₁:μ ≠ $ 13.50

Degrees of freedom γ = n-1 = 25-1 =24

The test statistic 't' is

substitute all values , we get

t = 1.399

This is calculated value  t = 1.399

The tabulated value of t are 5% level with 24 degrees of freedom

t = 1.710

Step 3:-

t = 1.399<1.710

Since calculated value < The tabulated value of t are 5% level with 24 degrees of freedom.

we will accepted the null hypothesis

the marketing manager decides to carry out a test of hypothesis

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.