$\backslash$table$[[$Mutual Funds $-$ Load,Return,Mutual Funds $-$ No Load,Return$],[$American National Growth,$15\mathrm{.}51,$Amana Income Fund,$13\mathrm{.}24],[$Arch Small Cap Equity,$14\mathrm{.}57,$Berger One Hundred,$12\mathrm{.}13],[$Bartlett Cap Basic,$17\mathrm{.}73,$Columbia International Stock,$12\mathrm{.}17],[$Calvert World International,$10\mathrm{.}31,$Dodge & Cox Balanced,$16\mathrm{.}06],[$Colonial Fund A$,16\mathrm{.}23,$Evergreen Fund,$17\mathrm{.}61],[$Common Sense Growth,$16\mathrm{.}04,$Fidelity Fund,$20\mathrm{.}61],[$Corefund Core Equity,$18\mathrm{.}77,$Forthis Advtg Cap App,$13\mathrm{.}38],[$Davis Convert Seurities,$18\mathrm{.}21,$Founders Blue Chip Fund,$17\mathrm{.}15],[$Deleware Small Cap,$17\mathrm{.}27,$Goldman Core Fixed Income,$18\mathrm{.}23],[$Dreyfus Premium Value,$11\mathrm{.}95,$Heartland Value,$18\mathrm{.}15],[$Federated Stocks & Bonds,$13\mathrm{.}81,$Janus Fund,$15\mathrm{.}82],[$First Invest FD for Income,$12\mathrm{.}44,$Manstay Cap Appriciation,$17\mathrm{.}29],[$Flag Inv Emerging Growth,$15\mathrm{.}39,$Merrill Spec Value,$16\mathrm{.}42],[$Fortis Equity Capital,$13\mathrm{.}46,$Mutual Beacon,$19\mathrm{.}49],[$FPA Capital,$23\mathrm{.}66,$Oberweis Emerging Growth,$11\mathrm{.}06],[$Franklin STR GL UT$,17\mathrm{.}38,$Paine Webber Growth & Income,$13\mathrm{.}89],[$Gabelli Value Fund,$22\mathrm{.}45,$Pimco Total Return,$15\mathrm{.}98],[$IDS New Dimensions,$18\mathrm{.}38,$Prudential Equity,$18\mathrm{.}29],[$John Hancock Growth & Income,$18\mathrm{.}06,$Putnam Growth & Income,$17\mathrm{.}80],[$Lord Abbett Dev Growth,$22\mathrm{.}75,$Royce FD Micro$-$Cap,$17\mathrm{.}05],[$Merrill Basic Value,$20\mathrm{.}35,$Scudder Development,$12\mathrm{.}80],[$MFS World Tot Return,$13\mathrm{.}09,$Smith Barney Appreciation,$15\mathrm{.}09],[$New England Growth Opp,$18\mathrm{.}16,$Stein Roe Capital Oppty,$19\mathrm{.}70],[$Oppenhmr Quest Small Cap,$14\mathrm{.}47,$T Rowe Price Balanced,$13\mathrm{.}57],[$Phoenix Worldwide,$15\mathrm{.}78,$Thompson Plumb Growth,$18\mathrm{.}58],[$Princor Bond,$8\mathrm{.}40,$USAAA Growth & Tax Strat,$11\mathrm{.}89],[$Stagecoach Disd Income,$16\mathrm{.}52,$Vanguard Equity Income,$19\mathrm{.}00],[$United Cont$1$ Income,$12\mathrm{.}59,$Vanguard Windsor,$20\mathrm{.}71],[$Victory OH Regional,$18\mathrm{.}24,$Vontobel Int$1$ Equity,$13\mathrm{.}56],[$Zweig SR TR Apprec,$14\mathrm{.}80,$Weith Value,$19\mathrm{.}82]]$ Load versus No$-$Load Mutual Funds. Mutual funds are classified as load or no$-$load funds. Load funds require an investor to pay an initial fee based on a percentage of the amount invested in the fund. The no$-$load funds do not require this initial fee. Some financial advisors argue that the load mutual funds may be worth the extra fee because these funds provide a higher mean rate of return than the no$-$load mutual funds. A sample of $30$ load mutual funds and a sample of $30$ no$-$load mutual funds were selected. Data in the file Mutual were collected on the annual return for the funds over a five$-$year period. The data for the first five load and first five no$-$load mutual funds are as follows.

For this case, we are interested in whether load mutual funds provide a higher rate of return than no$-$load mutual funds.

Before performing the test in excel, you can answer these:

$1.$ What are the appropriate null and alternative hypotheses for this application?

$2.$ What type of test would you run $($z$,$ t$,$ proportions$)?$ Why?

$3.$ Will this be a one$-$tailed or two$-$tailed test? If one$-$tailed, which direction are we interested in $($higher or lower$)?$

After performing the test in excel, you an answer these:

$4.$ Based on the results of the analysis, what is the value of the test statistic $($t or z$)$ for this test?

$5.$ What is the p$-$value? Use the p$-$value rejection rule to come up with the statistical conclusion.

$6.$ Based on your statistical conclusion, what is your recommendation $($English conclusion$)?$

DATA BELOW