1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Stels [109]
3 years ago
12

A company that produces laundry detergent is interested in the level of consumer awareness concerning the unique properties of t

heir product. Historical data indicated that among the consumers who buy this detergent, the proportion who purchased it because they had seen it advertised on TV is 0.80. The marketing manager feels that decreases in the TV advertising budget over the years has caused a decrease in sales. She decides to conduct a survey to determine if there is sufficient evidence to conclude that the population proportion is less than 0.80. In a random sample of 400 consumers who bought this detergent, 296 indicated that they bought it because they saw it advertised on TV. What is the value of the test statistic for the test described above and what is the type of alternative hypothesis?
Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
8 0

Answer:

The value of test statistic is -2.736.

The type of alternate hypothesis is Left- tailed.

Step-by-step explanation:

We are given that Historical data indicated that among the consumers who buy this detergent, the proportion who purchased it because they had seen it advertised on TV is 0.80. In a random sample of 400 consumers who bought this detergent, 296 indicated that they bought it because they saw it advertised on TV.

We have to test the hypothesis to determine if there is sufficient evidence to conclude that the population proportion is less than 0.80.

<em>Let p = population proportion of people who purchased the detergent because they had seen it advertised on TV.</em>

<em />

SO, Null Hypothesis, H_0 : p \geq 0.80  {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is greater than or equal to 0.80}

Alternate Hypothesis, H_a : p < 0.80  {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80}

The test statistics that will be used here is <u>One-sample z-proportion test;</u>

                      T.S. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = proportion of people who bought detergent because they saw it advertised on TV in a sample of 400 customers = \frac{296}{400} = 0.74

           n = sample of customers = 400

SO, <u>test statistics </u> = \frac{0.74-0.80}{\sqrt{\frac{0.74(1-0.74)}{400} } }

                               = -2.736

Therefore, the value of the test statistic for the test described above is -2.736.

<em>And the type of alternative hypothesis is left-tailed because we have to determine whether the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80.</em>

You might be interested in
By 8:00 a.m., the snack bar had made $3,256 in sales. By noon, the snack bar’s total sales were $8,821. On average, how much mon
Margaret [11]

Answer:

$1391.25 per hour

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
The table shows the relationship between the number that fit into given number of boxes from a bakery . What is the missing valu
ki77a [65]

Answer:

The missing value should be 48 because between the two numbers of each group. They are multplied by 6

Step-by-step explanation:

Hope this Helped!

7 0
2 years ago
Read 2 more answers
Use the table to write a proportion
Marizza181 [45]

Answer:

n = 17

\frac{n}{85}= \frac{34}{170}

Step-by-step explanation:

\frac{n}{85}= \frac{34}{170}

n · 170 = 34 · 85

170y = 2890

170y ÷ 170 = 2890 ÷ 170

y = 17

7 0
2 years ago
HOW TO CONSENTRATE ON STUDY?​
Ad libitum [116K]

Answer:

Listen to music or watch a video about what your about to study. Or do what I do... eat while studying

Step-by-step explanation:

4 0
3 years ago
Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increas
polet [3.4K]

Answer:

a) The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

Step-by-step explanation:

a) Develop a 90% confidence interval estimate of the population mean monthly rent.

Our sample size is 120.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

df = 120-1 = 119

Then, we need to subtract one by the confidence level \alpha and divide by 2. So:

\frac{1-0.90}{2} = \frac{0.10}{2} = 0.05

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 119 and 0.05 in the t-distribution table, we have T = 1.6578.

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

s = \frac{650}{\sqrt{120}} = 59.34

Now, we multiply T and s

M = T*s = 59.34*1.6578 = 98.37

The lower end of the interval is the mean subtracted by M. So it is 3486 - 98.37 = $3387.63.

The upper end of the interval is the mean added to M. So it is 3486 + 98.37 = $3584.37.

The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) Develop a 95% confidence interval estimate of the population mean monthly rent.

Now we have that \alpha = 0.95

So

\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025

With 119 and 0.025 in the t-distribution table, we have T = 1.9801.

M = T*s = 59.34*1.9801 = 117.50

The lower end of the interval is the mean subtracted by M. So it is 3486 - 117.50 = $3368.5.

The upper end of the interval is the mean added to M. So it is 3486 + 117.50 = $3603.5.

The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) Develop a 99% confidence interval estimate of the population mean monthly rent.

Now we have that \alpha = 0.99

So

\frac{1-0.95}{2} = \frac{0.05}{2} = 0.005

With 119 and 0.025 in the t-distribution table, we have T = 2.6178.

M = T*s = 59.34*2.6178 = 155.34

The lower end of the interval is the mean subtracted by M. So it is 3486 - 155.34 = $3330.66.

The upper end of the interval is the mean added to M. So it is 3486 + 155.34 = $3641.34.

The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain.

The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

4 0
3 years ago
Other questions:
  • What is the surface area of a sphere with a radius of 11 units?
    13·2 answers
  • Please help with this question. I appreciate it
    13·1 answer
  • In the figure, what is the value of z?<br> a. 2.9<br> b. 5.6<br> c. 6<br> d 8.75
    15·1 answer
  • Please help me please help me if you don't know gently move your hand
    10·1 answer
  • What does is the value of x in this problem
    14·1 answer
  • What are the first four terms of the sequence an=n2+4
    10·1 answer
  • A quarter is worth 1/4
    5·2 answers
  • DF and GI are parallel lines.<br><br> Which angles are alternate interior angles?
    10·1 answer
  • Please help me this is really confusing here's the question
    12·1 answer
  • Does anyone know the answer to this?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!