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Papessa [141]
3 years ago
14

According to a report released by CIBC entitled "Women Entrepreneurs: Leading the Charge," the average age for Canadian business

women in 2008 was 41. In the report, there was some indication that researchers believed that this mean age will increase. Suppose now, a few years later, business researchers in Canada want to test to determine if, indeed, the mean age of Canadian businesswomen has increased. The researchers randomly sample 97 Canadian businesswomen and ascertain that the sample mean age is 43.4. From past experience, it is known that the population standard deviation is 8.95. Test to determine if the mean age of Canadian businesswomen has increased using a 1% level of significance. What is the p-value for this test? What is the decision? If the null hypothesis is rejected, is the result substantive?
Mathematics
1 answer:
SOVA2 [1]3 years ago
4 0

Answer:

We conclude that the mean age of Canadian businesswomen has increased.

Step-by-step explanation:

We are given that according to a report released by CIBC entitled "Women Entrepreneurs: Leading the Charge," the average age for Canadian businesswomen in 2008 was 41.

The researchers randomly sample 97 Canadian businesswomen and ascertain that the sample mean age is 43.4. From past experience, it is known that the population standard deviation is 8.95.

Let \mu = <u><em>mean age of Canadian businesswomen.</em></u>

So, Null Hypothesis, H_0 : \mu \leq 41      {means that the mean age of Canadian businesswomen has decreased or remained same}

Alternate Hypothesis, H_A : \mu > 41     {means that the mean age of Canadian businesswomen has increased}

The test statistics that would be used here <u>One-sample z-test statistics</u> because we know about population standard deviation;

                               T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean age of Canadian businesswomen = 43.4

             \sigma = population standard deviation = 8.95

             n = sample of Canadian businesswomen = 97

So, <u>the test statistics</u>  =  \frac{43.4-41}{\frac{8.95}{\sqrt{97} } }

                                     =  2.64

The value of z test statistic is 2.64.

<u>Also, P-value of the test statistics is given by;</u>

             P-value = P(Z > 2.64) = 1 - P(Z < 2.64)

                           = 1 - 0.99585 = <u>0.00415</u>

Now, at 1% significance level the z table gives critical value of 2.33 for right-tailed test.

Since our test statistic is more than the critical value of z as 2.64 > 2.33, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <em><u>we reject our null hypothesis</u></em>.

Therefore, we conclude that the mean age of Canadian businesswomen has increased.

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Answer: (0.076, 0.140)

Step-by-step explanation:

Confidence interval for population proportion (p) is given by :-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

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n= sample size.

\alpha = significance level .

z_{\alpha/2} = critical z-value (Two tailed)

As per given , we have

sample size : n= 500

The number of Independents.:  x= 54

Sample proportion of Independents\hat{p}=\dfrac{x}{n}=\dfrac{54}{500}=0.108

Significance level 98% confidence level : \alpha=1-0.98=0.02

By using z-table , Critical value : z_{\alpha/2}=z_{0.01}=2.33

The 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters will be :-

0.108\pm (2.33)\sqrt{\dfrac{0.108(1-0.108)}{500}}\\\\=0.108\pm2.33\times0.013880634\\\\=0.108\pm0.03234187722\\\\\approx0.108\pm0.032=(0.108-0.032,\ 0.108+0.032)=(0.076,\ 0.140)

Hence, the 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters.= (0.076, 0.140)

8 0
3 years ago
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Answer:

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Step-by-step explanation:

6-3=3

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