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alexandr402 [8]
2 years ago
14

A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase s

ales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200.(Provide mathematical steps and explanations in detail to receive full credit.) The researcher would like to test the following hypothesis ????: ?? ? 8,000 ????: ?? > 8,000 (a) Calculate the value of the test statistic. Let ?=0.05 (b) What is the conclusion based on the critical value approach? Let ?=0.05 (c) What is the conclusion based on the P-VALUE value approach? Let ?=0.05
Mathematics
1 answer:
Ann [662]2 years ago
3 0

Answer:

a) Z= 0.0228

b) based on the critical value, it is a one tailed test

c) Since the p-value is less than the level of significance (α= 0.05) so we reject the null hypothesis.

This implies that the advertising campaign has been effective in increasing sales.

Step-by-step explanation:

The null hypothesis is H₀ : µ = 8000

The alternative hypothesis is H₁ : µ ˃ 8000

Mean (µ) = 8000

Standard deviation (σ) = 1200

n = 64

We will use the Z test to test the hypothesis

Z = (X - µ)/ (σ/√n)

Z = (8300 – 8000)/ (1200/√64)

Z = 300/ (1200/8)

Z = 300/ 150

Z= 2

From the normal distribution table,

2 = 0.4772

Φ(z) = 0.4772

Since Z is positive,

P(x˃a) =0.5 - Φ(z)

= 0.5 – 0.4773

= 0.0228

The required P-value = 0.0228

The P-value of one tail Z test at α= 0.05 level of significance

P-value = p(Z˃2.5)

= 0.0228

Since the p-value is less than the level of significance (α= 0.05) so we reject the null hypothesis.

This implies that the advertising campaign has been effective in increasing sales.

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You saved $20,000.00 and want to diversify your monies. You invest 45% in a Treasury bond for 3 years at 4.35% APR compounded an
Maru [420]

Compound Interest

A total of $20,000 is invested in different assets.

45% is invested in a Treasury bond for 3 years at 4.35 APR compounded annually.

For this investment, the principal is P = 0.45*$20,000 = $9,000.

The compounding period is yearly, thus the interest rate is:

i = 4.35 / 100 = 0.0435

The duration (in periods) is n = 3

Calculate the final value with the formula:

M=P_{}(1+i)^n

Substituting:

\begin{gathered} M=\$9,000_{}(1+0.0435)^3 \\ M=\$9,000\cdot1.136259062875 \\ M=\$10,226.33 \end{gathered}

The second investment is a CD at 3.75% APR for 3 years compounded annually. The parameters for the calculations are as follows:

P = 15% of $20,000 = $3,000

i = 3.75 / 100 = 0.0375

n = 3

Calculating:

\begin{gathered} M=\$3,000_{}(1+0.0375)^3 \\ M=\$3,000\cdot1.116771484375 \\ M=\$3,350.31 \end{gathered}

The third investment is in a stock plan. The initial value of the investment is

P = 20% of $20,000 = $4,000

By the end of the first year, the stock plan increased by 8%, thus its value is:

M1 = $4000 * 1.2 = $4,800

By the end of the second year, the stock plan decreased by 4$, thus the value is:

M2 = $4,800 * 0.96 = $4,608

Finally, the stock plan increases by 6%, resulting in a final balance of:

M3 = $4,608 * 1.06 = $4,884.48

Finally, the last investment is in a savings account at 2.90% APR compounded annually for 3 years (not mentioned, but assumed).

P = $20,000 - $9,000- $3,000 - $4,000 = $4,000

i = 2.90 / 100 = 0.029

n = 3

Calculating:

\begin{gathered} M=\$4,000_{}(1+0.029)^3 \\ M=\$4,000\cdot1.089547389 \\ M=\$4,358.19 \end{gathered}

To summarize, the final balances for each type of investment at the end of the third year are:

Investment 1; $10,226.33

Investment 2: $3,350.31

Investment 3: $4,884.48

Investment 4: $4,358.19

Total balance: $22,819.32

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1 year ago
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