Answer :
Answer:
a) test statistic, [tex]t_{s} = -4.20[/tex]
b) P-value = 0.0001
c) It can be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years
Step-by-step explanation:
There are 40 trading days, therefore, sample size, n = 40
Calculate the Sample mean:
[tex]\bar x = \frac{\sum x}{n} \\\bar x = \frac{4.153 +4.6228 + ...+...+5.4563}{40}\\\bar x = 5.5945[/tex]
Get the null and alternative hypothesis:
Null hypothesis, [tex]H_{0} : \mu = 7.52[/tex]
Alternative hypothesis, [tex]H_{a} : \mu \neq 7.52[/tex]
Calculate the sample standard deviation:
[tex]SD = \sqrt{\frac{\sum (x - \bar x)^{2} }{n - 1} } \\SD = \sqrt{\frac{(4.1531-5.5945)^{2} + (4.6228-5.5945)^{2}+...+ (5.4563-5.5945)^{2}}{39} } \\SD = \sqrt{\frac{327.6161}{39} } \\SD = 2.8983[/tex]
a) Calculate the test statistic:
[tex]t_{s} = \frac{\bar{x} - \mu}{SD/\sqrt{n} } \\t_{s} = \frac{5.5945 -7.52}{2.8983/\sqrt{40} }\\t_{s} = -4.20[/tex]
b) Calculate the P-value
Getting the P-value using the excel function:
P-value = (=T.DIST.2T(|ts|, df))
P-value = (=T.DIST.2T(4.20, 39))
P-value = 0.0001
c) If the level of significance, [tex]\alpha = 0.05[/tex]
The P-value (0.0001) < α(0.05), the null hypothesis is rejected.
It can therefore be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years