Scrooge-

In a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 38

Ganezh [65]

Answer:

a

$0.716 < p < 0.744$

b

$0.3498 < p < 0.4089$

c

With the result obtained from a and b the manager can be 95 % confidence that the proportion of the population that complained about dirty or ill-equipped bathrooms are within the interval obtained at a

and that

the proportion of the population that complained about loud or distracting diners at other tables are within the interval obtained at b

Step-by-step explanation:

From the question we are told that

The sample size is $n = 1003$

The number that complained about dirty or ill-equipped bathrooms is $e = 732$

The number that complained about loud or distracting diners at other tables is $q = 381$

Given that the the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = (100- 95)\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Considering question a

The sample proportion is mathematically represented as

$\r p = \frac{e}{n}$

=> $\r p = \frac{732}{1003}$

=> $\r p = 0.73$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }$

$E = 1.96* \sqrt{ \frac{ 0.73 (1- 0.73)}{1003} }$

$E = 0.01402$

The 95% confidence interval is

$\r p - E < p < \r p +E$

$0.73 - 0.01402 < p < 0.73 + 0.01402$

$0.716 < p < 0.744$

Considering question b

The sample proportion is mathematically represented as

$\r p = \frac{q}{n}$

=> $\r p = \frac{381}{1003}$

=> $\r p = 0.3799$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }$

$E = 1.96* \sqrt{ \frac{ 0.3799 (1- 0.3799)}{1003} }$

$E = 0.0300$

The 95% confidence interval is

$\r p - E < p < \r p +E$

$0.3798 - 0.0300 < p < 0.3798 + 0.0300$

$0.3498 < p < 0.4089$

8 0

2 years ago

Of 20 chickens, 9 are brown. What fraction is brown? (please show the working)

Novosadov [1.4K]

Answer:

9/20 also 45%

Step-by-step explanation:

well if 20 of them 9 are brown so 9 out of 20 of them are brown/45% of them because out of 20 each thing right or each person is 5%

8 0

2 years ago

Read 2 more answers

George gets a pay rise from £632 per week to £711 per week. What percentage pay rise was he given?

Colt1911 [192]

Answer:

12.5%

Step-by-step explanation:

£632 - 100%

£711 - ?%

?%= (711*100)/632 = 112.5%

112.5-100=12.5%

6 0

2 years ago

A salesperson works 40 hours per week at a job where she has two options for being paid. option a is an hourly wage of $19. opti

frez [133]

The two options are 2% and $38

7 0

2 years ago

I need help with every question I will give brainliest and everything if you do it thannkkkk uuuuu!

konstantin123 [22]

Answer: 1. 144

2. a

3. 790.05

4. 1.5

5. lenght width and height 4/5 = 24

Step-by-step explanation:

6 0

2 years ago